4th axis as a "poor man's lathe"

[A_Camera]

DC servo is breushed DC motor with attached encoder for feedback.
AC servo is kind of 3 phase BLDC motor with encoder for feedback.

Drives for both types of servo motors could, by design, ve connected to AC or DC power source (at the end it is ALWAYS DC source).

That's the way I see it as well. But perhaps others see it differently, and that's OK as long as we understand what we mean. Mine is the brushless, 3-phase delta wired motor which I think all AC servos are. As for the drivers, yes, in the end, ALL driven by DC but installation wise it looks easier if you just have to plug one into the mains directly, compared to having to have a large power supply first. On the other hand, if a driver needs like 80VAC then it needs a large transformer and a box anyway, so while building a PSU out of that to provide DC output is a tiny bit more work, but that's really no big deal and in my opinion the benefits are basically gone. But sure, if directly mains driven then it is really nice and neat solution. Unfortunately, those motors are still pretty expensive.