==> Does vocabulary include why the word is chosen or just the defnition of the word?
I don't think so. You cannot choose a word if it's not in your vocabulary, but why one word is chosen over another word is more a matter of semantics.
A grammar, especially formal grammars, are the rules that explain how the specific words of a langugage can be put together to build a well-formed sentence. In and of itself, grammar doesn't speak to the meaning.
The homework ate the dog.
There is nothing grammatically wrong with that sentence, although it has no semantic value. Punctuation is used to remove semantic ambiguity, or otherwise clarify intent.
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