The former is associated with heart / pulse. The latter relates to throat / breath.
This is historical though. Etymology can often give us insights into a word, but can also lead us astray. While it's less likely to use the term for a brief incident that wasn't fatal, the use doesn't relate to the heart or pulse at all.
Are ‘Asphyxiation’ and ‘Suffocation’ exactly same in both meaning and nuance?
The same in meaning, different in nuance. If it's technically correct to use one, it's technically correct to use the other, but there are times when one is more likely than the other (including a few where it's technically incorrect!)
The biggest difference is that because native speakers tend to learn the word suffocation at a younger age than asphyxiation, and because it's been in the language longer, it's more common in less formal registers. Suffocation would still be found in formal speech, but someone might deliberately choose asphyxiation to affect a more educated tone ("Look at me, I know big words like asphyxiation!").
Asphyxiation will be used pretty much independently of means.
There are causes of asphyxiation for which while we may use suffocation, we are less likely to; drowning, hanging, strangulation. In these cases we're more likely to use the specific word.
(Note, this doesn't make us more or less likely to use asphyxiation - it just adds another common word that we might use where we would otherwise decide to favour suffocate over asphyxiation; so rather than choosing between asphyxiation and suffocation we're choosing between asphyxiation and drowning).
While the above are causes of asphyxia that are less often called suffocation, smothering by covering the mouth and nose is very often referred to as suffocation. Chest compression that blocks the lungs from functioning is also quite often called suffocation, especially in crowd disasters (we don't have a single non-technical term for it), and since burking (the murder method of choice for someone planning to sell the body to an 19th Century Scottish anatomy lecturer) combines both, it would also be very often covered by suffocation (more so than burking, which is not a well-known word).
We're also very likely to use suffocation when it was caused by fumes or gasses blocking oxygen from the lungs (as happens with smoke in fires). This was the case in the reports you mentioned, and as you noted some went with suffocated and some with asphyxiation.
There are a few cases that are technically not suffocation/asphyxiation, but were which might be referred to as suffocation, but it would be unlikely for them to be referred to as asphyxiation.
Hanging and strangulation can cause injury or death not just by asphyxiation, but by blocking carotid arteries and jugular veins which cuts off the supply of oxygen to the brain, but not to the body and so is not asphyxiation. This might be called suffocation anyway.
Hanging can also cause death by breaking the neck, and as a means of capital punishment is often designed to kill in this way to be more humane - or alternatively to not kill like this to be a harsher punishment - with the British for example consulting the Official Table of Drops to work out how much rope for how heavy a convict. If this was clearly the case (you'd seen them swing and heard a snap), it would be unusual to call it suffocation, but if someone was discovered hanging it just be assumed that they had suffocated.
(A very large a drop can cause decapitation, but that tends to be a lot more obvious as to what happened).
Again though, calling a hanging suffocation isn't that common in the first place.
Air poisoning—where it was the toxicity of what was inhaled that injured or killed someone, rather than the lack of oxygen—might also be mistaken for suffocation, and therefore called that. For one thing, it might not be possible to tell which effect actually caused death, and for another some may not understand the difference between suffocating because the air breathed lacks oxygen, and air poisoning.
We're more likely to use suffocation than asphyxiation for a non-fatal case, and all the more so if it didn't even need medical treatment (but the people giving it that medical treatment would be more likely to use asphyxiation).
We're more likely to use asphyxiation in a technical context.
We're similarly more likely to use asphyxiation in terms of a medical examination into the cause of death, even if we're not such experts themselves. ("The hospital said he died of asphyxiation" rather than "The hospital said he suffocated").
We're more likely to use the verb suffocated than asphyxiate, especially transitively. So "he suffocated" a bit more than "he asphyxiated", and "she suffocated him" much more than "she asphyxiated him".
We're much more likely to use asphyxiation in terms of hypoxyphilia, including in its other name of erotic asphyxiation. Yet another term for it is asphyxiophilia which is clearly related. (That said, fetishists quite often have very strong likes or dislikes for words associated with the target of their fetish, and while I haven't heard of this in terms of hypoxyphilia, I don't know a lot of open hypoxyphiliacs, but have observed a similar thing in terms of other fetishes, so it could be possible that some practitioners would always use suffocation).
In all, the above is so long not because the words are different, but because they are so much alike - so I can think of lots of little differences when one might be favoured over the other, rather than any clear-cut rule.
The main difference again is just that children would know suffocate before they learned asphyxiation, and that gives them a slightly different register, and different tendency to be used precisely or carelessly. In all, they still refer to the same thing.
Some background on the difference between 'nonchalant' and 'insouciant'
Before focusing on the meanings of the two words, let's take a look at the Ngram chart for nonchalant (blue line) versus insouciant (red line):
According to Merriam-Webster's Eleventh Collegiate Dictionary, nonchalant entered English (directly from French) circa 1734, whereas insouciance—the noun form of insouciant—arrived (also directly from French) in 1799. The Ngram chart suggests that nonchalant has been several times more common than insouciant in published English texts for the past 150 years or so. Even so, I was somewhat surprised that the Eleventh Collegiate doesn't give insouciant a separate entry. Here are its entries for nonchalance and nonchalant:
nonchalance n (1678) : the state or quality of being nonchalant
nonchalant adj {F[rench] fr[om] pr[esent] p[articiple] of nonchaloir to disregard, fr[om] non- + chaloir to concern, fr[om] L[atin] calēre to be warm —more at LEE} (ca. 1734) : having an air of easy unconcern or indifference syn see COOL — nonchalantly adv
And here is its entry for insouciance:
insouciance n {F[rench], fr[om] in- + soucier to trouble, disturb, fr[om] O[ld] F[rench],fr[om] L[atin] sollicitare — more at SOLICIT} (1799) : lighthearted unconcern : NONCHALANCE — insouciant adj — insouciantly adv
The synonyms note under the entry for cool discusses a group of similar adjectives: cool, composed, collected, unruffled, imperturbable, and nonchalant. Considering that MW views insouciance as meaning "lighthearted unconcern: NONCHALANCE," The exclusion of insouciant from the cluster of synonyms allied with cool is surprising and disappointing. The note on nonchalant in the entry under cool reads as follows:
NONCHALANT stresses an easy coolness of manner or casualness that suggests indifference or unconcern {a nonchalant driver}
This very much of a piece with the discussion of nonchalant in Webster's Dictionary of Synonyms (1942):
Nonchalant stresses an easy coolness of manner, or casualness that suggests, rather than necessarily implies, indifference or unconcern: it often connotes lightheartedness; as, "God...knows, if he is not as indifferent to mortals as the nonchalant deities of Lucretius" (Byron); "Dallying with a cigar, which he smoked nonchalantly as he sang (T. E. Brown); "He walked in a nonchalant fashion" (D. H. Lawrence).
Meriam-Webster's Dictionary of Synonyms (1984) repeats its 42-year-older predecessor's entry almost word for word, except tht it drops the phrase "rather than necessarily implies" and replaces the T.E. Brown quotation with this one:
at the back {of the ambulance}, haughty in white uniform, nonchalant on a narrow seat, was The Doctor—Sinclair Lewis
And yet the entry for nonchalant in Webster's Fifth Collegiate Dictionary (1936/1941) is quite different from the one that appears in Webster's Ninth Collegiate Dictionary (1983), which is identical to the entry (noted above) in the Eleventh Collegiate. Here is the Fifth Collegiate's entry:
nonchalant, adj. ... Lacking in warmth of feeling, enthusiasm, or interest; indifferent; also, Colloq[uial], casual and imperturbable.
The Fifth Collegiate's entry for insouciance, meanwhile, contains this information:
insouciance, n. ... Want of concern; indifference, esp[ecially] as an attitude of mind
In effect, such difference as remains between nonchalant and insouciant in 1941 seems to reflect the difference in their French roots—nonchalance suggesting indifference through a lack of warmth or concern, and insouciance suggesting indifference through an absence of care or troubledness. The meanings are clearly very close, in any case.
One reference work that does provide discussions of both nonchalant and insouciant is S.I. Hayakawa, Choose the Right Word: A Modern Guide to Synonyms (1968). But rather unexpectedly, Hayakawa assigns the two words to different synonym groups: nonchalant lands in a group headed by flippant; and insouciant falls into group under jaunty.
Here are the relevant comments from these two discussions:
flippant, casual, flip, fresh, nonchalant, sassy, smart, wise These words are all all used to describe particular kinds of attitudes, speech, and behavior. ... Unlike [flippant, flip, sassy, and fresh], casual and nonchalant can be neutral or even complimentary in tone. Both words indicate a lack of concern, interest, or excitement: a casual air; a nonchalant approach to business problems. Nonchalant, however, may suggest an attempt to be disciplined or detached: All during the meeting, Mr. Jessup maintained his nonchalant manner, even when the shouting and arguing were at their height.
...
jaunty, chipper, debonair, insouciant These words are used to describe a brisk unworried, self-assured person or the way in which he acts. ... Insouciant translates literally from the French to mean without care; it also suggests gaiety of manner and sophistication: the insouciant young bohemians who travel from on party to another without a thought for tomorrow.
Here again, the distinction between the two words seems to rest primarily on a perceived difference between lack of concern (nonchalant) and lack of care (insouciant). Hayakawa seems to think that the former reflects an attitude while the latter reflects a spirit; I'm not at all persuaded that he is right.
My answers to the poster's specific questions
With regard to the poster's specific questions, I offer these answers:
1. To judge from the foregoing discussions of the meanings of insouciant and nonchalant, the difference between "a nonchalant shrug" and "an insouciant shrug" might be imperceptible to an objective viewer, although we might expect the insouciant shrug to be a bit more vigorous (because it expresses a carefree attitude) than the nonchalant shrug (which is likely to be muted by the shrugger's lack of concern for whatever has prompted the shrug.
2. Ogden Nash seems to be using the words nonchalance and insouciance without a great deal of regard for their overlap in meaning. He is aiming for comic effect and so is happy to use two words where one would convey the essential notion of cucumberish imperturbability.
3. Nash uses nouciance as a ludicrous spelling for nuisance, nothing more. A similar joke spelling for the sake of a rhyme appears in his famous short poem, "If called by a panther/ Don't anther."
4. As for the sentence "He was (nonchalant/insouciant/blithe) about the poor living conditions of the animals in his farm," I wholeheartedly agree with Edwin Ashworth's comment (beneath the question) that none of the three named options is as suitable as indifferent would be and that a change in preposition from about to to would further improve the sentence:
He was indifferent to the poor living conditions of the animals in his farm.
In my view, indifferent indicates a level of coldness toward potential suffering that the other terms—with their emphasis on disposition (blithe), attitude (nonchalant), or spirit (insouciant)—are ill equipped to convey.
Best Answer
There is no difference in core meaning, and even the connotational penumbrae overlap a lot. It's mostly about the attitude you're trying to convey; and this is going to depend more on each reader's actual experience with the words than with any broad consensus.
Here's how I would use them:
But that's a very personal view; others may feel differently.