I see several synchronous machines have an actual rotation speed at less than synchronous speed e.g. synchronous speed is 1800 rpm and the actual rotation is 1780 rpm. However, we don't call it slip instead we call it droop. Why? What is the difference between slip and droop?
"Slip" is a term used to describe the difference between synchronous speed and actual speed in induction motors. Slip is always present in induction motors, because the rotor speed must always be lower than synchronous speed to induce the rotor field.
The amount of slip for a given load is not equal for all motor designs, and if more than one motor is connected to the same load, motors with differing slip will not share the load equally. An engineer may want to specify the percentage of load from each motor when running two different motors sharing the same load. The controller(s) would be set up to measure the currents, infer the torques, and reduce the frequency of one of the motors to share the load as desired. This "artificial slip" would be set so that the other motor would take up the desired portion of the load. In motor controller terminology, this addition of slip is called "droop" control.
The converse is also true. In the generator world, "droop" refers to the reduction in speed (and frequency) that a generator would experience when loaded if the input did not change. Once again, it is important because when multiple generators are on the same grid, generators have differing droop as they are loaded, so the generator with the lowest droop would otherwise tend to pick up most of any additional load. Droop control is necessary so that the load is shared; each generator must increase its governor setting to "catch up" and stay closely in phase with others on the grid so that load sharing will occur.