The story
From horse + power: the unit was originally defined as the amount of power that a horse could provide. Both non-metric and metric units of power were derived from effectively identical measurements of the power a draught horse could sustain over several hours, with the difference in watts solely due to different rounding errors to express that power in round numbers in the original non-SI units (ft·lbf/min and kgf⋅m/s respectively).
Etymology from Wiktionary, CC BY-SA 4.0.