AFAIK:
Under G-reg, if on a Transport CofA, you need to run a journey log. This is addition to any personal logbooks.
The maintenance requirements are separate: a logbook for airframe, engine, VP prop (3 logbooks).
A "tech log" is a thing run by flying schools, and
AFAIK is not a legal requirement, but they use it to get an instant picture of what is going on across the fleet. It is also used to record fuel status and has been implicated in the worst fuel management practices on the PPL training scene, with the most spectacular recent fuel exhaustion accident on a plane owned by an AOC holder