Exactly. UNIX time, GPS time, and TAI are a fixed offset from one another. They're a variable offset from UT1 (based on earth's angle with respect to some distant quasars). If you care about things like where the stars are, use UT1. If you want monotonic time, use TAI or one of the time standards that's a fixed offset from it. If you want to plan a spacecraft trajectory through the solar system, use barycentric coordinate time (TCB). If you want something that approximates UT1 but otherwise works like TAI, use UTC.

If you're dealing with human activity, UTC will usually be the easiest choice. If you're just dealing with computers, TAI (or one of its fixed-offset variants like UNIX time) will usually be the easiest choice.