...in either federal or state a majority means the same thing. None of the recent presidents have had a majority of the votes, that is why we have the electoral college.
...also the election of a congressman or senator for the US House or Senate is a state election and is not a federal election. State election laws apply. Ages to vote etc. If it were a federal election people could just drive over and vote.
...and as long as we are on the subject, the election of the president is an election by the states, not a federal election.