To become a member of the Supreme Court of the United States, an individual is appointed by the President and must be confirmed by the Senate. So, the correct process is presidential appointment and Senate approval.
The process typically involves the President nominating a candidate for the Supreme Court, followed by a confirmation hearing held by the Senate Judiciary Committee. After the hearings, the full Senate votes on whether to confirm the nominee. If the nominee receives a majority of votes in the Senate, they are confirmed and can assume their position on the Court.