vote vs ballot

vote and ballot both are nouns.

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

As nouns, vote and ballot are synonyms defined as:

vote and ballot: a choice that is made by counting the number of people in favor of each alternative

Other synonyms of vote include balloting, voting.

As verbs, ballot is a hyponym of vote; that is, ballot is a word with a more specific, narrower meaning than vote:

vote: express one's preference for a candidate or for a measure or resolution; cast a vote
ballot: vote by ballot

Other hyponyms of vote include write in, turn thumbs down, vote down, outvote, poll.

vote (noun)	ballot (noun)
a choice that is made by counting the number of people in favor of each alternative	a choice that is made by counting the number of people in favor of each alternative
the opinion of a group as determined by voting	a document listing the alternatives that is used in voting
a legal right guaranteed by the 15th amendment to the US Constitution; guaranteed to women by the 19th amendment
the total number of voters who participated
a body of voters who have the same interests

vote (verb)	ballot (verb)
be guided by in voting	vote by ballot
express one's choice or preference by vote
express a choice or opinion
bring into existence or make available by vote
express one's preference for a candidate or for a measure or resolution; cast a vote