The term 'reproducible' in 'reproducible build' (https://reproducible-builds.org/) conveys "bit-for-bit identical output". -- The benefit of that is security; others can compile the same sources and check that they get the same binaries.
But more generally, 'reproduce' just means 'create the same thing again'.
Nix uses "reproducible" in a more general sense: you provide the same inputs, and you'll get a program which behaves the same way, regardless of whether you compiled from source or downloaded binaries from a cache.
IMO, I think "reproducible build" is enough to unambiguously refer to the former. But, if you can think of a nicer word for "you get the same behavior from the same inputs" than "reproducible", it would be worth suggesting.
