They are called running mates when they are running for election.
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The President & Vice-President are elected by the ballots cast by citizens called electors.
vice president, Joe Brown
The power that is vested in the President and the Vice President is called executive power. This power is expected to be exercised according to the constitution.
The person that is known is the vice president.
The vice president serves as president of the senate. There are 100 Senators, and if there is ever a tie in the senate, the vice president gets to cast the winning vote. If the vice president is not available, somebody else will serve, he is called the president pro tempore.