What you are thinking of is the difference between prescriptive linguistics and descriptive linguistics. Descriptive linguistics is all about what people use (how people talk, how they write, how many loops go on this letter, what they feel sounds correct, etc.). Prescriptive linguistics is when someone comes in (often a teacher) and decides what correct language is and is not.
According to the article What Is 'Correct' Language? from the Linguistic Society of America:
Descriptive grammarians ask the question, "What is English (or another language) like—what are its forms and how do they function in various situations?" By contrast, prescriptive grammarians ask "What should English be like—what forms should people use and what functions should they serve?" Prescriptivists follow the tradition of the classical grammars of Sanskrit, Greek, and Latin, which aimed to preserve earlier forms of those languages so that readers in subsequent generations could understand sacred texts....
A general rule of thumb is that if you are seeing discussion of "right" and "wrong" vocabulary, grammar, prosody, etc., in the context of some people using language the "wrong" way, then you are dealing with a prescriptive linguist. Descriptive linguists don't deal with "right" and "wrong", they deal with "what people actually use" and "what people don't use".