How does removing a prime minister differ from removing a U.S. president?

The removal of a prime minister and a U.S. president differs fundamentally due to the structure of their respective governments.

Prime Minister: Vote of Confidence

In parliamentary systems, the prime minister and their cabinet serve only as long as they maintain the support of the legislative majority. A prime minister can be removed through a vote of confidence, a procedure where the legislature expresses its disapproval of the government.12
* Mechanism: If the government loses a vote of confidence or a motion of censure, it must resign.21
* Variations: In some countries, such as Germany and Spain, a "constructive" vote of no confidence is required, meaning the legislature can only oust a prime minister if they simultaneously agree on a successor.21

U.S. President: Impeachment

The U.S. president serves a fixed term and is not dependent on legislative support to remain in office. Removal is a rare, legalistic process reserved for serious misconduct.345
* Mechanism: The House of Representatives must first impeach the president (charge them with "Treason, Bribery, or other high Crimes and Misdemeanors"), followed by a trial in the Senate.3
* Threshold: Conviction requires a two-thirds majority vote in the Senate, making it a significantly more cumbersome and difficult process than a parliamentary vote of no confidence.53