demurrer vs objection

demurrer and objection both are nouns.

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

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

demurrer (noun)	objection (noun)
a defendant's answer or plea denying the truth of the charges against him	(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
(law) a formal objection to an opponent's pleadings	the act of protesting; a public (often organized) manifestation of dissent
(law) any pleading that attacks the legal sufficiency of the opponent's pleadings	the speech act of objecting
	the act of expressing earnest opposition or protest