Comparisons between the two systems can only go so far, because of the different ways each system treats the relationship between the executive and legislative branches - those differences are the fundamental distinction between a parliamentary system and the congressional system. In the Congressional system, there is a strict separation of powers, while in the parliamentary system, the executive and the legislative branch overlap.
So for example, Tony Blair has never won a nation-wide election to the office of Prime Minister (such office not having any legal existence). He’s won the party leadership of the Labour party through that party’s organizational structure, and then he’s led the Labour party to successive majority governments in the general elections, where the Labour party has elected a majority of MPs to the local constituency, including Blair himself, who won in his constituency. As leader of the majority party, he becomes Prime Minister by the appointment of the Queen. So in Britain, the leader of the executive becomes head of government because he controls the legislative branch.
Similarly for the Cabinet - both the U.S. and the U.K have Cabinets, but they’re very different beasts. The U.S. Cabinet secretaries are non-elected. They’re there because the President appointed them, and they hold their office at his pleasure.
That’s not the case with the U.K. Cabinet - the members of the Cabinet are members of the House of Commons, and have been elected by the people of their constituencies. The Prime Minister has appointed them to the Cabinet, but his choices of Cabinet ministers are circumscribed by internal party politics. He has to make sure that the Cabinet is generally representative of the party as a whole, even if that means making one of his strongest personal rivals in the Labour party the Chancellor of the Exchequer. And if he alienates too many members of his own party, they can kick him out before the next election, as Prime Minister Thatcher discovered.
The cabinet ministers are responsible for their departments much the same way as Cabinet secretaries are in the U.S., but they are responsible not to the P.M., but to Parliament. As well, the Cabinet takes collective responsibility for all government decisions - they’re not just the decisions of the Prime Minister, but of the government as a whole. A Cabinet minister who opposes a decision around the Cabinet table nonetheless has to speak in favour of it once taken, or resign from Cabinet.
And not all offices have direct analogues between the two systems. The Lord Chancellor is a good example (at least, until Blair abolishes the office, as he’s talked about doing.) The Lord Chancellor is a member of the House of Lords and presides over it during legislative debates. Since the House of Lords is also the highest court for the U.K., the Lord Chancellor also participates in the judicial decisions. And the position of Lord Chancellor is also part of the executive, so there’s a new Lord Chancellor any time the government changes.
There is an Attorney General, but he’s not a member of Cabinet and doesn’t run a department. The U.K. Attorney General is the chief law officer of the Crown, responsible for giving legal advice to the Cabinet and representing the Crown in the courts. While the Attorney General of the U.S. is responsible for similar legal issues, he is also the top law enforcement officer in the federal system, with responsibility for the FBI and the federal marshals. In the U.K., some of those functions are handled either locally, or through the Home Secretary.
Another office that has the same name but completely differnt functions is the Speaker. In the U.S., the Speaker of the House is the leader of the majority party in the House, and makes decisions on a partisan basis. In the U.K., the Speaker is elected to a constituency, like other M.P.s, and then elected to the Speaker’s chair by the House of Commons. Oncle elected Speaker, he/she is expected to run the House on a non-partisan basis - I think they resign from their party, and in subsequent general elections run unopposed by the major parties - can’t remember if that’s still the case.
