Comment by the__alchemist

Phrased in a slightly different way, assuming the standard is Betaflight/Ardupilot/PX4. (This article uses BF): Inner PID rate loop; this compares IMU-measured rates vs that commanded by manual controls. This might run at 1-4kHz.

On top of this (Maybe at a few hundred hz), you can add outer controls to set attitude. This could be an autopilot, or having the controls command attitude instead of rate. Betaflight pilots usually don't both with this, and have the simple setup of control maps to rate.

I've programmed firmware using a weird hybrid where the controls command a change in the target attitude. So it flies like rate, but has the forced attitude stability of an attitude-based control system. Non-standard, but makes it so you don't need to worry as much about tuning the PID loop. In practice, you can do full aerobatic flight with this like you'd do with a rate-only setup. (Basically, there is a commanded attitude quaternion; controls nudge it; the PIDs update motor power to maintain this commanded quaternion.)