Why does englad ave a prime minister and the us have a preident?

It shows how they get their office. In a democracy, a President will always be elected directly, and they will always be the figurehead of the country. In the US, the President has major responsibility for having laws enacted, as the leader of the executive branch. In many European countries, they have a President who is just a figurehead. The British Monarch has a similar role, but the Prime Minister is the person who runs the government.

A Prime Minister is always appointed by a President or Monarch. Since the legislative assembly has to agree to this choice, the process is generally a formality. In the UK, the leader of the ruling party in the House of Commons always becomes the Prime Minister.