smart vs act up

smart is a noun but act up is not a noun.

Word	Noun	Adjective	Verb	Adverb
smart	Yes	Yes	Yes	No
act up	No	No	Yes	No

As verbs, act up is a hyponym of smart; that is, act up is a word with a more specific, narrower meaning than smart:

Other hyponyms of smart include bite, burn, sting, burn, itch, hunger, thirst, throb, shoot.

smart (noun)	act up (noun)
a kind of pain such as that caused by a wound or a burn or a sore

smart (adjective)	act up (adjective)
showing mental alertness and calculation and resourcefulness
capable of independent and apparently intelligent action
quick and brisk
improperly forward or bold
characterized by quickness and ease in learning
painfully severe
elegant and stylish

smart (verb)	act up (verb)
be the source of pain	make itself felt as a recurring pain
	misbehave badly; act in a silly or improper way