The same servo drive, the same motor, the same PID math — but which variable the innermost loop is told to hold constant changes everything about how the axis behaves.
Every modern servo or BLDC drive can run in at least three control modes, and picking the wrong one is one of the most common reasons a mechatronic axis feels "wrong" even though the tuning gains look fine. Position, velocity, and torque control aren't three different algorithms — they're the same cascaded PID structure with the command target moved to a different rung of the ladder. What the loop is told to hold at the commanded value determines what the system does when it meets a disturbance it didn't expect: a jam, a collision, an external push, a changing load.