Earlier quoted context omitted.
> Languages definitely follow grammars But it's the other way around! Grammars follow languages. Or, more precisely, grammars are (very lossy) language models. They describe typical expectations of an average language speaker. Grammars try to provide a generalized system describing an average case. I prefer to think of languages as a set of typical idioms used by most language users. A given grammar is an attempt to…
This is a terminological difference. Linguists use "grammar" as a technical term for a speaker's implicit knowledge of how their language works. That knowledge could be statistical or rule-based in nature, although most linguistic theories say that it's rule-based. You're using grammars to mean human-produced descriptions of that knowledge.
Grammars the way I understand them are are a family of human language models. Typically discrete in nature. The approach was born out of Chomsky's research culminating in the Universal Grammar idea.