Dictionaries, as their makers keep telling us, are descriptive. They tell how people use words instead of how somebody should use them.
That, however, does not restrict me and shouldn't restrict you. What is coyly called on this forum the "N word" should be in a dictionary; that doesn't mean that you should use it.
Now, when Roget made his thesaurus, he put in block 542.1 both "kindergarten" and "postgraduate school."
You can see how those ideas are closely related; each is a grouping of learners by age and proficiency.
On the other hand, nobody who speaks English would call them synonyms.
It's nice that somebody took the effort to bring similar ideas together, but people who use his book mostly use it to find words they can use.
You have a word that almost describes what you want; you look it up in the back to find the number; then you look under the number to find words describing similar things, conditions, or acts to those described by that word.
Competitors decided that this process would be more efficient if the similar words were listed under the first word alphabetically. Fine
Many used the word "thesaurus" to describe their arrangement. Not fine. A few have used "Roget's Thesaurus" to describe their arrangement. Outroght fraud.
Dictionaries list this as one meaning of "thesaurus." Again, that is fine. Some people use the word that way, and dictionaries report how the words are used. They aren't in the business of distinguishing between honest usage and fraudulent usage.
More than half the time that a paint can is opened, it is opened with a screw driver. People have developed tools specifically for opening paint cans; they don't call them "screw drivers."
Now for something slightly different.
If you know a word, and another actually has the same denotation and the same connotation, why in the world would you use the other word?
OTOH, this almost never occurs. So, a "list of synonyms" is a list of words that might mean what you want to mean, and might not. So a writer should never look in a thesaurus or a list of synonyms for a fresh word.
Some of us, especially Uther, have a decent recognition vocabulary but a use vocabulary which often fails him. Then, I can look in the thesaurus for words that I recognize as meaning closer to what I want to say than the word which I can actually recall.
(Uther's memory is failing, and he's old. The second, however, did not cause the first. Back when I was an undergraduate, I took a test in German class on translating a story into English -- usually my strong suit. I could not think of the word "crate." Finally, I used "box." The story, however, took place in a boxcar, and it was definitely a crate. That's one time I could have used a thesaurus, or even a synonym list.)
As I said earlier, one can also get into a situation in which your story needs more detail than you have in your head. Then, it's perfectly fair to look up a list of e.g. carriages. After that, though, you need to seek descriptions until you are certain of what you have.
Does that carriage normally come with a driver? Where?