Learn English – An easier way to describe the phrase “people relevant to the current situation”

There are a lot of different kinds of infinitive. The infinitive to smoke in

• He stopped to smoke.

(as Colin and Fluffy have already pointed out) is a Purpose infinitive, a kind of adverbial clause answering Why?, which one may introduce with in order to, or move to the front of the sentence,

• He stopped in order to smoke.
• In order to smoke, he stopped.

in order to distinguish it from more common types of postverbal infinitive, like the to smoke in

• He began/started to smoke.

which is an infinitive object complement clause, a kind of noun clause that is the direct object of began or start, representing the activity (or when generic, the habitual activity) that the subject began or started.

Begin and start are also alike in that they can take infinitive complements, like the sentence above, as well as gerund complements, like the one below

• He began/started smoking.

which is synonymous with the second sentence.

However, stop, unlike begin and start, does not allow an infinitive complement, though it does allow a gerund. Thus, any infinitive following stop can't be an infinitive complement clause, and the next likely reading is as a purpose infinitive clause.

Both are common uses for stop, and this little curlicue helps distinguish them. English, and every language, like anything alive, is full of baroque details like this.

It's more biology than linguistics but it sounds like learned or acquired reflex.

a reflex which is learned through practice or repetition and may involve both a far more complicated set of triggering stimuli and a far more complicated pattern of motor response,

e.g., the reflexive motor actions produced after one has learned to ride a bicycle or drive a car; most such reflexes are somatic because they involve complex response patterns from skeletal muscles.

There is also a psychological term: Unconscious competence

The individual has had so much refining practice with a skill that he or she does not really need to think about what to do. It has become "second nature" and can be performed with very low frequency of errors.

Because the skill is not occupying much of the individual’s conscious thoughts, it can often be performed while executing another task. The individual has become so comfortable with the skill she/he will often be able to teach it to others.

Based on your edits, it is related with Curse of knowledge also:

The curse of knowledge is a cognitive bias according to which better-informed people find it extremely difficult to think about problems from the perspective of lesser-informed people.