An office holder-elect does not exercise the powers of his or her office until he or she takes the oath. In the meantime, the politician will usually assemble a "transition team" of some sort, to prepare for a smooth transfer of power following the inauguration. The outgoing office holder is called a "lame duck" while serving the remainder of his or her term.
In the United States, the members of the U.S. Electoral College are elected in November once every four years, and the Electoral College in turn elects the President of the United States in December, and finally the President-elect assumes office in January. One is officially the president-elect only after being chosen by the Electoral College, but unofficially the person chosen in the November election is called the President-elect even before the Electoral College meets. An example of the practical effect of the official status is found in the U.S. Constitution's provision that if the President-elect dies, then the Vice President-elect becomes president on Inauguration Day. That rule takes effect only after the meeting of the Electoral College. If the person unofficially called the President-elect dies before that meeting, then the Electoral College would have broad discretion to choose some other person.
When a politician is not elected, he or she is usually called the "designate" until formally assuming office. For example, the "Secretary-designate" or the "Vice President-designate." This title is occasionally used for Prime Ministers as well, to reflect the fact that they are not usually directly elected, but instead formally appointed by the Head of State according to the rules of the Parliamentary system.