hurrah vs cheer

hurrah and cheer both are nouns.

Word	Noun	Adjective	Verb	Adverb
hurrah	Yes	No	Yes	No
cheer	Yes	No	Yes	No

As nouns, cheer is a hypernym of hurrah; that is, cheer is a word with a broader meaning than hurrah:

hurrah (noun)	cheer (noun)
a victory cheer	the quality of being cheerful and dispelling gloom
	a cry or shout of approval

hurrah (verb)	cheer (verb)
shout `hurrah!'	become cheerful
	spur on or encourage especially by cheers and shouts
	show approval or good wishes by shouting
	cause (somebody) to feel happier or more cheerful
	give encouragement to