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Originally the VP was whoever got the second most votes. Then the 13th Ammendment happened. Now in most states (all states) the President and VP run as a pair but the Electoral Delegates vote for them separately.

Can the delegates vote for one and not the other? Depends. Traditionally you cast your delegate vote according to the results so you'd vote along "ticket" lines. In some states delegates ( who are often put forward by the parties) are bound to vote according to the election results. In some states they are not. Traditionally they do but as we saw last US election we aren't even pretending to be doing sane things anymore.