ache vs act up

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

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

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

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

ache (noun)	act up (noun)
a dull persistent (usually moderately intense) pain

ache (verb)	act up (verb)
have a desire for something or someone who is not present	make itself felt as a recurring pain
be the source of pain	misbehave badly; act in a silly or improper way
feel physical pain