The best term I've found so far is descriptive grammar.
In linguistics, the term refers to the syntactical forms in common use by native speakers. This is not prescriptive grammar, a term typically used by linguists to refer to the set of rules we learn to follow in HS English or when studying English as a second language. However, in the linguistic fields of language acquisition and prescriptive linguistics, the term is used and prescriptive grammars are studied and developed, but it is important to note that there is no official standardizing body for English in any English speaking country, and there is robust and often passionate debate within and outside these fields about what is acceptable or not.
Prescriptive English grammar has not generally kept up with the conceptual development of descriptive grammars in linguistics, nor for that specifically related to English. Prescriptive grammar is a mess, and the grammar traditionally used in teaching English is often proscriptive and typically relies on many outdated and conflicting resources, which results in many unnecessary obstacles for language learners.
From the Advanced English Dictionary (online app)
prescriptive linguistics: an account of how a language should be used instead of how it is actually used; a prescription for the `correct' phonology and morphology and syntax and semantics
Karl Hagen: member profile
Here's a link to his his website.