A couple of other comments on the differences between US and UK governments.
The US is the canonical example of a "presidential" system, while the UK government is the canonical example of a "parliamentary" system. The US federal government consists of three distinct branches: executive, legislative and judiciary. The President is head of the executive branch.
Unlike the UK and other countries with the parliamentary system, the President is not a member of Congress; he/she is separately elected for fixed 4-year terms (maximum of two) independent of Congress. This gives the US President considerably more independence than a UK Prime Minister, who is out of power whenever his party loses control of the House of Commons.
The Congress can still remove a US President from office through impeachment, but by design this is a difficult and time-consuming two-step process; it is not a matter of simply passing a vote of no-confidence and calling for early elections. First, the House of Representatives votes to impeach by a simple majority, analogous to a grand jury returning an indictment. The process then moves to the Senate, which holds a trial. Conviction requires a 2/3 vote. This is a very high bar, especially today.
Only two US presidents have ever been impeached: Andrew (not Lyndon) Johnson and Bill Clinton. Neither was convicted in his Senate trial. One president (Nixon) resigned to avoid almost certain impeachment and conviction. The same process can (and has) been used to remove federal judges, who normally serve for life, but again it is very difficult and time-consuming so it has only been done a few times, usually after a judge has been convicted of a serious crime like bribery.
Much time is spent in US civics classes explaining the "separation of powers" and "checks and balances" on which the US federal government is based. Most state governments have a very similar structure, though the specific names are different. The President can propose legislation to Congress, and as Bob mentioned, if he refuses to sign it into law after both houses have passed it Congress can override that veto with a super-majority vote.
One of the President's most important roles is to appoint federal judges who serve for life to give them independence from day-to-day politics, but they must be confirmed (approved) by the Senate. He also appoints ambassadors, cabinet members (what you'd call "ministers") and agency heads, also with Senate approval. The President conducts foreign policy, but treaties must also be ratified by the Senate before they take effect. (The House has no role in confirming appointments and treaties).
Although the President commands the military, in principle he cannot declare war; that power is reserved for Congress. However, since the mid-20th century the President has usurped much of Congress's war-making power; this has been a perennial issue ever since the Vietnam War.