The answer is etymology.
Many English words are built from a stem and some prefixes and suffixes. (I think this is true of most languages.) There are many suffixes that preserve the core idea of the word, and give it a particular grammatical nature and a particular meaning. For example, from the stem defin-, you can build the verb define (to give something a definition), the noun definition (the act of giving something a definition, or the outcome of this act), the (uncommon) noun definer (someone or something that defines), etc.
Many of these stems, prefixes and suffixes existed in ancestor languages of English. Many of the resulting words existed in ancestor languages, and sometimes different words in the same family evolved differently.
The examples you give are quite illustrative. The verb define comes from the Latin verb definire, and the noun definition comes from the Latin noun definitio. The verb combine comes from the Latin verb combinare, and the noun combination comes from the Latin noun combinatio. Note how one pair has the infinitive verb ending in -are and the noun ending in -atio, and the other pair has the infinitive ending in -ire and the noun ending in -itio. What happened here is that the ending of the verb was eroded: Latin verbs had over a hundred different endings depending on the mood, tense and person, whereas English has 5. Many verb endings got simplified to -e (often in French before they reached English), which erased the previous vowel. So what happened isn't that defin- got the suffix -ition and combin- got the suffix -ation, but rather that defini- and combina- both lost their ending vowel.
Although many stems of this type end with the vowel -a or -i, Latin also had the vowel e, as in. delere, which gave the English words delete and deletion through a less direct route). Some stems had no final vowel, e.g. cedere (many forms of the verb, including the infinitive, have an additional -e- to ease pronunciation), giving cede in English, and the associated noun cessio (whence cession) where the suffix and the final consonant had merged together and diverged already in an ancestor language of Latin.
The suffix -tion to form a noun from a verb, meaning the action itself or the outcome of this action, was very common in Latin (shown in the form -tio above, but the -n was already present in some cases) and in French (also spelled -tion) but it is no longer productive in English.
English has many other suffixes, some of them productive, most of them not. Most of these suffixes come from Latin, often through French, even though English is primarily a Germanic language. The reason for this is historical: German was the language of ordinary people (who mostly use existing words to designates objects from everyday life), French and Latin were the languages of learned people (who invent new concepts and make up words for them).
Best Answer
1) The boulder came to rest=the boulder stopped moving
2) To put an issue to rest=to stop discussing the issue, to "put it aside", to make it stop being a problem where the issue is seen to be moving
3) To lay someone to rest= to bury a person's body in a cemetery.
Those are all verbs, not nouns. 1) come to (s) rest means to no longer move.
1) means X will no longer be moving.
2) means to put something out of sight, to make it stop being a problem, to have it stop.
3) is an euphemism where death is seen as place where there is no more movement AND a situation where, if you are tired, you can rest. It's a double meaning. compare: I laid the sick dog on the bed so he could rest. There is no double meaning there. It has the meaning of 5) below.
4) "to rest the horses" means to stop them moving so they can recover their energy because they are tired.
5) "the blames rests with x" means the blame can move no further to another person because it stops at your father.
In fact, all these uses relate to stopping some kind of movement. And the trick is that in the last case, it means stopping movement and recovering energy: He rested on the bed for two hours.
Now that you have the single meaning (stopping movement) and the second meaning (stopping movement and recovering energy to be able to move once again), you can see which meaning is intended.
{EDIT to original answer] 6) Come to rest is a V to V structure: come to rest, come to see, come to understand, etc. Those are all verbs. Therefore, so is rest in this case.