nag vs complain

nag is a noun but complain is not a noun.

Word	Noun	Adjective	Verb	Adverb
nag	Yes	No	Yes	No
complain	No	No	Yes	No

As verbs, complain is a hypernym of nag; that is, complain is a word with a broader meaning than nag:

Other hypernyms of nag include kick, kvetch, plain, quetch, sound off.

nag (noun)	complain (noun)
an old or over-worked horse
someone (especially a woman) who annoys people by constantly finding fault

nag (verb)	complain (verb)
remind or urge constantly	express complaints, discontent, displeasure, or unhappiness
bother persistently with trivial complaints	make a formal accusation; bring a formal charge
worry persistently