There are many differences in vocabulary (not to mention spelling) between American English and British English. Some of these differences are because the Pilgrims took Elizabethan English over to the New World with them, and retained many of its words, which then fell out of use in Britain.
English is spoken very widely around the world, and has developed into several varieties. British Commonwealth countries tend to use British English (Australia, Canada, New Zealand, India, South Africa, etc), but each of these countries has developed its own dialects, accents, vocabularies, and spelling conventions. The two main varieties we're going to look at here are British English and American English.