Difference between grants and awards
I think you basically answered your own question: grants are something where you apply and get money based on what you say you will do. Awards are something you get for work you already did. Some awards do not include any money. I doubt you'll find an authoritative document, because there's no organization that sets rules for the entire academic community. I could image a certain amount of overlap/fuzz, so there could be things that one school/organization calls a grant that somewhere else might call an award.

A confusing additional fact is that the term "award" is also often used as a verb applied to the noun "grant", as in "Professor X was awarded a grant for . . .".  I would not call this "an award" in the noun sense; it is a grant, and "awarding a grant" means "giving a grant" or "deciding who gets a grant".  To me "an award" is the sort of thing described with "Professor X won the ABC Award for . . ."

Here is a page talking about grants vs. "gifts" that restates some of the distinctions you already mentioned, but this is just one accounting context at one university.