This is a difficult question to answer, because both aches and pains are subjective experiences - like colours - which you're unable to share, but assume everybody understands. I would have assumed that every language has words for both ache and pain, so a dictionary would tell you the difference in an instant. But, I would also assume you've done that, so your native language might not (I'm interested to find out what language that is).
An ache is a persistent discomfort, typically dull so that you can try to ignore it, but sometimes all-encompassing, yet not sharp enough to describe as pain. Your legs would ache after a tough run; you would not describe this as pain. You usually get a headache, not a head pain. You would suffer pain when you cut your finger, then experience an ache as the wound heals.
A pain is something more localised, often (but not always) short-lived, and something you'd be less able to ignore.
When you receive an injection, there is a pain as the needle goes in. During the following days, the surrounding area will ache.
There is considerable overlap between the two, and it would be quite acceptable to say "the ache in my shoulder is painful".
Poets and songwriters quite often speak of their heart aching. This fits well with a persistent sense of yearning or melancholy. If they said there was a pain in their heart, it would suggest a quite different emotion.
Describing pain and discomfort is difficult and subjective; I imagine in any language. When a doctor asks you how much something hurts, how can you explain in a reliable way?
I found this usage note under the word rebuke in NOAD; you may find it helpful:
rebuke, admonish, censure, reprimand, reproach, scold: All of these verbs mean to criticize or express disapproval, but which one you use depends on how upset you are.
If you want to go easy on someone, you can admonish or reproach, both of which indicate mild and sometimes kindly disapproval. To admonish is to warn or counsel someone, usually because a duty has been forgotten or might be forgotten in the future (e.g., admonish her about leaving the key in the lock), while reproach also suggests mild criticism aimed at correcting a fault or pattern of misbehavior (e.g., he was reproved for his lack of attention in class).
If you want to express your disapproval formally or in public, use censure or reprimand. You can censure someone either directly or indirectly (e.g., the judge censured the lawyer for violating courtroom procedures; a newspaper article that censured “deadbeat dads”), while reprimand suggests a direct confrontation (e.g., reprimanded by his parole officer for leaving town without reporting his whereabouts).
If you're irritated enough to want to express your disapproval quite harshly and at some length, you can scold (e.g., to scold a child for jaywalking).
Rebuke is the harshest word of this group, meaning to criticize sharply or sternly, often in the midst of some action (e.g., rebuke a carpenter for walking across an icy roof).
Also, of the three words that you've mentioned, I think censure most stongly implies that some sort of formal disciplinary action has been taken. Admonish would entail a verbal warning only, at least in my mind. Reprimand could be used either way, as someone might be verbally reprimanded by a supervisor or mentor, or else formally reprimanded, which could result in some kind of formal documentation in a work file.
Best Answer
You can have more and less accurate. It is the closeness to a target. Rifle shooters are awarded points in order of accuracy to the bulls'eye. The accuracy of the description from the eyewitness with bad eyesight, was very low.
Precise relates to very fine detail - how carefully measured (or described) something is. You can be precise and not accurate. I have two watches. One with only hours minutes, but the other gives seconds also, so more precise measuring of time. ( I wish it was digital and even more precise to 0.1 seconds measurement). Anyway, I missed my 9:00am train every morning for a week using the more precise watch! How ? Every day I arrived at the train platform very precisely at 8:54:49 (+/- 1 second) - repeatedly - I am very measured! However, I kept missing the train! Why? Well because the time on the watch had not been set accurately - it was 15 minutes out from the true time - inaccurate. I was measuring precisely ( to the nearest second) but was not at all accurate in my time measurement. Precise but not accurate. A person can give a precise (detailed ) description of a location (bench, path, fence, gate , tree, rock, etc) - but be totally inaccurate to the actual location (on a map say, or street name in a town) of an event.
"I am writing a blog that has a title "Love and Lust". I want to point out that it is more accurate/precise to say that the title should be "Romantic Love and Lust", as there are three kinds of love."
Perhaps the words you want are less ambiguous (more defined, more clear):
I want to point out that it is less ambiguous to say that the title should be "Romantic Love and Lust", as there are three kinds of love.
Otherwise I think I would go with both - precise (more detailed description) and accurate :
I want to point out that it is more precise, and accurate, to say that the title should be "Romantic Love and Lust", as there are three kinds of love.