It entirely depends on the design of the system. “Fly-by-wire” just means that the surfaces are controlled electronically, not by physical cables. What the electronics are actually doing varies wildly by airplane.
The simplest/oldest versions just command control surface position, exactly the same as non-fly-by-wire. This doesn’t give you any new functionality but may result in lighter, higher performing, easier to maintain system.
You can write the software to command whatever you want. In pitch that can be angle of attack, pitch rate, g-force, elevator position, etc. A fairly common pitch law is called “C*”, a blend of pitch rate (at low speed) and g-force (at high speed).
In roll it could be aileron position, roll rate, bank angle, etc. The one that most closely imitates a well behaved conventional airplane is roll rate.
For rudder it can be rudder angle, sideslip angle, yaw rate, etc.
Which is the “right” choice depends, a lot, on what the airplane is for and how you want it to feel to the pilots.
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