George Bush and Tony Blair's jobs come with different powers. Here are some reasons why:
1. In the USA, people vote for the person they want to be president. They do this by picking the members of an electoral college, that formally appoints him or her. In the UK, people vote for MPs who support a political party, the leader of the party with most MPs then becomes the prime minister.
That means the president can make decisions on their own because people have voted for them personally, whereas the prime minister is expected to discuss things with other ministers and MPs from their party.
2. The prime minister picks their cabinet from Members of Parliament. The president can pick anyone they like (as long as they are approved by the US Senate).
That means they can pack it full of people who will support their policies, giving them a lot more strength when making decisions.
3. The president is also the USA's head of state, in the UK that job is done by The Queen.