It sounds as though you are saying "colloquialism[s]" have some value or relevance to technical understanding of a process.
It seems to me this is the primary means by which information gets lost because people think they know what is meant, but they don't.
It's the stumbling block that always reoccurs.
---- If someone says "map" and means function, then I know what a function is (I think).
If someone says "map" and means a higher order function, like in programming, then that's also something I think I know.
If someone wants to talk about morphisms that are not functions, then that sounds like it may be beyond my ability to follow.
But in any of the three cases, using the word "map" out of context fails to tell me which it is. Other associations, like the paper rand-mcnally map that I once used to drive across the country, are not helpful.
Nor have I for that specific context. As Whitman noted, people are large and contain multitudes. Reclassification and transcription are certainly common enough colloquialism even if not formal processes. It's all mappings[0] in the end.
> everybody kind of nods along while never agreeing on what the arrows mean.
Yes, this is what I said, and elucidated an abstraction process to convey complex technical information I both experienced and have used in practice.
[0] https://en.wikipedia.org/wiki/Map_(mathematics)