There are many words, here are a couple of them:
phraseology
1.the manner in which words or phrases are used
Collins Dictionary1.manner or style of verbal expression; characteristic language:
legal phraseology.
Random House Kernerman Webster's College DictionaryA particular mode of expression, especially one characteristic of a particular speaker or subject area.
‘I know that my phraseology and way of putting things is sometimes a bit direct.’
Oxford Living Dictionaries
There is also "register". "register" doesn't necessarily have to do with formality, class and social status, but often does, at least more often than "phraseology". It's also a bit more jargonistic, ie., specific to study of language.
1.(Linguistics) a form of a language associated with a particular social situation or subject matter, such as obscene slang, legal language, or journalese.
Collins Dictionary9.A variety or level of language used in a specific social setting: speaking in an informal register; writing in a scientific register.
American Heritage Dictionary