The energy a fixed pump wastes over the relief valve. A fixed pump makes full flow whenever it turns, and anything the circuit does not need becomes heat. A variable pump destrokes to produce only what is demanded, which saves fuel or electricity and reduces the cooling capacity the machine needs.

A control that destrokes the pump when system pressure reaches a set value, so the pump holds that pressure while delivering whatever flow the circuit takes. It is the simplest variable control and suits systems working at one pressure with varying flow demand.

Load sensing maintains a small fixed margin above the actual load pressure rather than holding a fixed setpoint, so the pump follows real demand moment to moment. It is more efficient than pressure compensation because the pump never generates more pressure than the load currently requires plus the margin.

Capping the product of pressure and flow so the pump cannot demand more power than the prime mover can supply and stall it. It is essential wherever a small engine or motor drives a large pump, and it lets the pump use the full available power across a range of pressures rather than being sized for the worst case.

Yes, and they usually are - load sensing with torque limiting is the standard mobile machinery arrangement. The combination gives efficient flow matching while protecting the engine, and most modern variable pumps are supplied with a compensator assembly offering several functions together.

Yes, and setting it correctly matters as much as choosing it. A load sensing margin set too high wastes much of the efficiency the pump was bought for; set too low it makes the system sluggish or unstable. Commissioning the compensator is part of installing the pump, not an afterthought.

Where the duty cycle includes idle or part-flow periods, generally yes - the energy saving and reduced cooling repay the difference. On a machine that runs at full flow continuously, a fixed pump is simpler and cheaper and there is nothing for the variable control to save.