Most of the great jazz players learned on an acoustic piano, and indeed continue to play on an acoustic piano. Hancock, Charles, Peterson, Jarrett, Corea, ... I can't recall a single jazz pianist of note that avoided an acoustic piano and/or built their technique off of semi-weighted keys. Folks like Peterson eventually dabbled and mastered certain electronic instruments, and most jazz musicians encounter electronic instruments as a significant part of their career, but they began with an acoustic.

Keyboards of all sorts are used in all manner of places. Jazz especially loves the rounder tones offered by "e-pianos". There are even some famous synthesized classical pieces. So they're undoubtedly useful instruments, just seemingly avoided in most conventional approaches to learning to play piano.

These are interesting facts that don't address the enormous space of options that exist between the dichotomy you originally presented. That said, please play whatever keyboard you enjoy and call it whatever you want to.