The United States of America operates as a federal presidential constitutional republic government. The President, Congress, and federal court system share power according to the United States Constitution.
The United Kingdom operates as a unitary parliamentary constitutional monarchy. The monarch is the head of state and the Prime Minister is the head of government. The British government has executive power, the Parliament of the UK/ the House of Lords/&Scottish Welsh and Irish Parliaments hold legislative power, the judicial system is the Supreme Court of the United Kingdom.
The British monarch is not voted into office by the people like the US President.