casting vote vs ballot

casting vote and ballot both are nouns.

Word	Noun	Adjective	Verb	Adverb
casting vote	Yes	No	No	No
ballot	Yes	No	Yes	No

As nouns, ballot is a hypernym of casting vote; that is, ballot is a word with a broader meaning than casting vote:

casting vote: the deciding vote cast by the presiding officer to resolve a tie
ballot: a choice that is made by counting the number of people in favor of each alternative

Other hypernyms of casting vote include balloting, vote, voting.

casting vote (noun)	ballot (noun)
the deciding vote cast by the presiding officer to resolve a tie	a choice that is made by counting the number of people in favor of each alternative
	a document listing the alternatives that is used in voting

casting vote (verb)	ballot (verb)
	vote by ballot