Yeah we have three branches of government.

Executive Judicial Legislative

The President heads the executive branch. The Legislative branch is split into the Senate (2 representatives from every state) and Congress (number of representatives depicted by state population size). (The Vice President actually sits in the Senate and can be used as a tie-breaker (101 votes instead of of 100 senators). The Leader of the House (Congress) is third in line for the presidency. The judicial branch is mostly known to be the Supreme Court but also contains the Federal Judicial Center.

Basically. For a law to exist you have to get a Majority vote from Congress and the Senate. Then the president signs it into law, or can Veto it. (If Congress has 2/3 vote the president veto would be overwrote). Same is required to amend the constitution itself (2/3)

Also if the people don't feel representatives have gotten their issue to the floor there are petitions. If a petition gets a lot of signatures it requires a formal response by the legislature. During the Obama administration he opened a website called We The People that allowed signatures for petitions and if 100,000 signatures were garnered it was required to get a formal response. This website was shut down during the first Trump administration in 2018.

So the Judicial branches job is to review any bill being signed into law and ensure it is not in conflict with previous laws, or deemed "unconstitutional" which would block the law and send it back to the legislature requiring them to acquire a 2/3 vote to amend the constitution where it conflicts.

The legislative branch also holds the power to oust the President if they overstep. Essentially if over 50% of Congress believes the president should be removed they can impeach him. Which sends it to the Senate. (Most every president has removed themselves upon a majority of Congress but they aren't required to yet). When it goes to the Senate they hold a trial. A 2/3 vote of the Senate implements the presidents removal. (The Republicans in the Senate did not vote to remove Trump, and thus they never had 2/3s of the vote and he refused to step down.). John Tyler and Richard Nixon both resigned before the Senate voted.

In the US, people consider any public sector job to be working in/for the government. Judges, Legislators, the president, TSA security, Park Rangers, Cops, Clerks at the driver's license office, etc. would all be considered government roles. Sometimes you need to clarify if you mean federal government or state government.

The president, his staff, and his political appointees are called the administration.