[canjobear]

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.

[vkazanov]

That's correct.

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.