Majority, plurality are arbitrarily defined in the United States, especially by statute, when they refer to an excess of votes as determining an election.
Both imply an excess of votes over the next highest candidate. The distinction between the two words applies when there are three or more candidates; then the person who is elected by a majority has more votes than the other candidates combined, that is, his vote is in excess of half of the total number of votes cast, and his majority is the number of votes cast for him in excess of one half of the total number of votes.
A person is elected by a plurality when he has more votes than any other candidate, whether he has a majority of the total or not. Thus, if a total of 290,000 votes are cast in an election contested by three candidates, with candidate A polling 200,000 votes, candidate B polling 75,000, and candidate C polling 15,000, candidate A wins the election by a majority of 55,000, and by a plurality of 125,000 over candidate B, and by a plurality of 185,000 over candidate C.
Sometimes, where the successful candidate has a vote that exceeds the total of votes cast for all opposing candidates, the term plurality is applied to this excess; thus, in the example given, while candidate A's majority is 55,000, his plurality over candidates B and C together is 110,000.