mutter vs complain

mutter is a noun but complain is not a noun.

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

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

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

mutter (noun)	complain (noun)
a complaint uttered in a low and indistinct tone
a low continuous indistinct sound; often accompanied by movement of the lips without the production of articulate speech

mutter (verb)	complain (verb)
make complaining remarks or noises under one's breath	express complaints, discontent, displeasure, or unhappiness
talk indistinctly; usually in a low voice	make a formal accusation; bring a formal charge