The one obvious answer is that in british national politics there are three political parties of some prominence, but in America there are only two.
There are also other differences in that in America there are federal and state legislatures, though with devolved parliaments in Britain that difference is not so obvious any more. More officials are elected in The United States than in The United Kingdom. One thing about the american political setup that is a direct copy of the situation in Britain in the eighteenth century is the Presidency. The powers of the president of the USA are almost exactly the same as those exercised by King George III.
For devotees of the British Constitution, like me, there has been a regretable slippage towards a more american way of doing things in recent years. I can cite the replacement of the judicial powers of the House of Lords with a "Supreme Court", and the impending replacement of The House of Lords, altogether, with an elected senate. Where will it all end?