tempo vs bpm

tempo and bpm both are nouns.

Word	Noun	Adjective	Verb	Adverb
tempo	Yes	No	No	No
bpm	Yes	No	No	No

As nouns, bpm is a hyponym of tempo; that is, bpm is a word with a more specific, narrower meaning than tempo:

tempo: the rate of some repeating event
bpm: the pace of music measured by the number of beats occurring in 60 seconds

Other hyponyms of tempo include beats per minute, M.M., metronome marking.

tempo (noun)	bpm (noun)
the rate of some repeating event	the pace of music measured by the number of beats occurring in 60 seconds
(music) the speed at which a composition is to be played