complaint vs objection

complaint and objection both are nouns.

Word	Noun	Adjective	Verb	Adverb
complaint	Yes	No	No	No
objection	Yes	No	No	No

As nouns, objection is a hypernym of complaint; that is, objection is a word with a broader meaning than complaint:

complaint (noun)	objection (noun)
an expression of grievance or resentment	(law) a procedure whereby a party to a suit says that a particular line of questioning or a particular witness or a piece of evidence or other matter is improper and should not be continued and asks the court to rule on its impropriety or illegality
(formerly) a loud cry (or repeated cries) of pain or rage or sorrow	the act of protesting; a public (often organized) manifestation of dissent
(civil law) the first pleading of the plaintiff setting out the facts on which the claim for relief is based	the speech act of objecting
(criminal law) a pleading describing some wrong or offense	the act of expressing earnest opposition or protest
an often persistent bodily disorder or disease; a cause for complaining