Some of both disciplines can be applied. I, and I suspect many amateur musicians don't have the ear or talent to transcribe Jazz Piano solos. So I've bought many of the available published transcriptions and use them as the basis for working out my own variations and/or improvisations. Alternatively I may be brave and try and play them as written.

A heinous crime I'm sure, but I'm an amateur and know my limitations.

Simon

Casio PX-S3000
Korg SV2S (73)

ABRSM Grade 7 distinction 2023.
Decent blues/rock Pianist.
Try to play Jazz Piano, but pretty rubbish.
Studying ABRSM grade 8 now.