> Would you say that "algebraic variety" is some incredibly common terminology just because it's common within a globe spanning subgroup?
Leaving aside that it came up often enough back in the early 1980s when I was working on the first draft of Magma (known then as Cayley) and having discussions with John Cannon, Charles Leedham-Green and George Havas, I would not say that it's as common among mathematicians to use the term as it is among air travellers and pilots to use city codes.
All air travel workers deal with destination codes, generally on a daily basis.
Not all mathematicians work with Abstract Algebras.
> I'm not finding this discussion especially enlightening.
Agreed. Your example certainly struggled for relevance.