I think as Brimshack said, it's about the way you elect governments.
In the USA, you have fixed terms for President and Congress; so the people you elect aren't there permanently, but they're there for a definite time. Also, you can have a change in Congress and have the same President and Cabinet. And who gets into Congress bears no direct relationship to who becomes President and the Cabinet.
In the UK and other parliamentary democracies like Australia, we don't have fixed terms. An election could be held at any time. And we can have a change of members of the Cabinet, and even the party governing, without an election. Or the Prime Minister could be desposed within their own party and someone else could take over. Our governments are formed and run in the following way:
- An election is held, at which all the members of the House of Representatives (or Commons in the UK) stand, aiming to represent an electorate, a geographical area with X number of people. They're called "MPs", for "Member of Parliament."
- We also elect the Senate, but the Senate has no part in forming a government. Like the Senate in the USA, it represents the states, with each state returning 12 Senators. The British House of Lords is part-elected, part-appointed by the Queen, and it too has no part in forming a government.
- The Governor-General (or Queen in the UK) then looks at the election results, and sees which individual commands the confidence of Parliament. This is usually whoever leads a party which gets more than half the House seats; but it could be someone from a party with less than half the seats, provided they can get some other party to support them on budgets and Votes of Confidence, this gets called a "minority government".
- The Governor-General invites the leader of that party to form a government; the leader becomes Prime Minister, and appoints Ministers, who must be members of the House or Senate.
- The Prime Minister selects their Ministers (of Defence, Justice, etc) who must be MPs or Senators.
- Individual House seats may come up for "byelections" if some MP resigns or dies before the next general election.
- Traditionally, the party decides its policies, and then every MP of that party will vote for that policy in Parliament; they may disagree with a particular bill, but they agree to vote for it anyway, since at some later time some other bill which a few party MPs disagree with will come up. From time to time a party MP may break ranks on some matter important to them, this is called "crossing the floor" since traditionally party MPs sit together, and to vote against the party an MP would physically cross the floor of Parliament.
- Parliament has a thing called Question Time, where MPs may ask questions of Ministers. The Opposition (those not in government) use this time to attack the government of the day; the government MPs use this as a time to praise it, "Can the Minister for Defence please tell the House about the fine work done by our soldiers in Iraq?" "I thank the Member for Bentleigh for his question, and..."
- Laws are passed by being initiated in the House, passed with a simple majority there, then passed in the Senate also. The Governor-General then signs them into law. In theory, the Governor-General may refuse assent to any law; unlike the USA, this cannot be overturned by Parliament. In practice, the Governor-General's powers are never used, would only be used for something truly obscene like, "Act for Consolidating the Criminal Code (2007) Henceforth, all crimes are punishable by death."
- The Prime Minister may be deposed as leader of their party by a Caucus meeting; the Caucus is all the members of the PM's party who are members of the House or Senate; if a majority of them turf the PM out as leader of the party, the PM is out, and whoever the party puts in is in.
- The Prime Minister may be deposed as PM in the House of Representatives by means of failing a Vote of Confidence. If the PM is truly dreadful and unpopular, usually their own party will depose them, as above. If the PM and whole Cabinet is unpopular, you just have to wait until the next election. However, if the PM's party doesn't have a majority in Parliament, either because they're a minority government or they lost the majority through a byelection, they may lose a Vote of Confidence. If they do, then we go back to the third step, the Governor-General seeing who can form a government. If no-one can manage it, the Governor-General issues writs for a general election.
- A general election must be held at least every three years in Australia, but the PM can ask the Governor-General to call one at any time. In practice, elections come early if the government is popular.
So you can see that in parliamentary democracies, the government is less permanent than in the USA's presidential republic. Just imagine that the various Secretaries of Defense, Treasury, etc had to be Congressmen or Senators, and that the US President could be questioned directly in Congress every day it sat, and if they lost a vote in the House they could be tossed out...!
You can see that in the USA, the leader of the government and the Cabinet are not directly answerable to the Congress; whereas in parliamentary democracies, they are, they have to visit there every day it sits, have to be in there jockeying for position amongst all those MPs. So the US keeps its actual day-to-day government separate from its body passing laws; the parliamentary democracy puts them together. That's why the US needs to distinguish between the "administration" (whoever's in charge today) and the "government" (the President + Cabinet + Congress). In a parliamentary democracy, the government and the administration are the same people.