Three completely different mathematical questions about the same error signal — not three volume knobs on one correction.
Ask someone to describe what "tuning Kp, Ki, and Kd" means and a common answer is some version of "making the correction stronger or weaker." That undersells what's actually happening. Every PID controller is continuously computing one thing — the error, e(t) = setpoint − measured value, over and over, every scan cycle. P, I, and D aren't three strengths of that one number. They're three genuinely different mathematical features extracted from the exact same error signal — its current value, its accumulated history, and its rate of change — and each one solves a piece of the control problem that the other two literally cannot.