tempo vs rubato

tempo and rubato both are nouns.

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

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

Other hyponyms of tempo include accelerando, allegretto, allegro, andante, meno mosso.

tempo (noun)	rubato (noun)
the rate of some repeating event	a flexible tempo; not strictly on the beat
(music) the speed at which a composition is to be played