A 'pump' is an assembly of a wet end and an electric motor. Electric motors and the impellers found in a wet end can be listed/rated by horsepower (HP) but these two ratings are not calculated the same way. Often the impeller HP is lower that that of the motor.
In 2012, most spa pump manufacturers changed the way pumps are rated. Most pumps are now assigned both an operational horsepower (ohp), and a total horsepower (thp) rating. The majority of older pumps used only the operational horsepower or a 3rd rating called BHP.
If you are replacing an older hot tub pump, be sure to match the operational hp rating rather than the total hp. To find the correct replacement pump, match the amperages as closely as possible (and voltage too).
The Amperage/HP will vary slightly on Emerson, Century & US Motor (Nidec) pump motors.
The listed amperage and motor of the pump you receive MAY differ from the one you are trying to replace.
Due to these factors motor HP is an unreliable method to determine a replacement.