Nominal means almost the same thing as rated. However ratings generally have tolerances and limitations attached to them. Motor have a nominal speed and voltage. The primary ratings will pertain to that same speed and voltage. The nominal power rating for a motor is the mechanical output power that it can safely produce at that speed and voltage. The mechanical output power will be stated is either horsepower or kilowatts depending on the standards applied.
The motor may be able to operate at other speeds and voltages and have specifications stating what power is safe for those speeds and voltages. Operating under those conditions may be considered as operating within the motor's ratings even though they are not the nominal operating conditions.
Generator ratings are similar to motor ratings. The nominal power would be the rated output electrical power stated in watts.
The nominal power and the power stated in the primary ratings is the output mechanical power for motors and electrical power for generators. A generator or motor is likely to have an efficiency rating. The input power may be left to be determined using the efficiency and output power ratings.
AC generators have both a maximum output power and a maximum output current or minimum power factor rating. For safe operation, neither the maximum power nor the maximum current can be exceeded.