What do you call the language-variation that a group of people speak with each other in a certain setting?
It's a language variety that adheres to all the rules and framework of the original language, and can be classified by certain idiosyncrasies and differences in the turns of phrase that have become idiomatic among that group of people because of their environment.
For example, academicians speak one style of English. I don't think it's correct to consider it a dialect.
As was pointed out to me humorously in a YouTube video and its comments, mathematicians can be identified by their style of speaking, using "namely", "more precisely", "trivial", and other phrases more often than other English speakers.
Young people say "if I recall correctly", "as far as I ___", "for the win", "that feeling when", "today I learned" etc., more commonly than other speakers because of back-translating the internet acronyms they're used to using, and apply patterns of speech gained from immersion in online communication and meme culture.
Similarly, in the corporate world "action" has become a verb that means something like "progress"/"move forward with"/"deal with".
What do you call these specialised versions of a language?
It is not a "jargon" because, to me, "jargon" only refers to the words and phrases that are used, it would not be correct to use it as a name for a type of language variety.
Based on what I understand of its Wikipedia page, the correct term also doesn't seem to be "vernacular", which seems closer in meaning to dialect.
I also don't think it is a dialect because it is not as diversified as a dialect. Dialects would normally be different in grammar, vocabulary, or pronunciation. But I am just interested in a language variety that is far more similar, adherent to, the original language.