There are many differences. The most obvious differences are in pronunciation; American accents are very different from British accents. Try listening online to Fox News (US) compared to BBC News (British). There are slight differences in spelling. For example, colour (British) instead of color (US). There are also differences in word usage and idiom. For example, the vegetable called aubergine (British) instead of eggplant (US). And there are some other minor differences in sentence construction and punctuation, but these are not so obvious or important to most people.

Самая заметная разница между британским и американским английским - это акценты. Британский звучит как-то чопорно, вычурно и отточено. Также характеризуется обильными изменениями в тональности в момент речи. Американский английский звучит более ровно в плане тональности, почти как спокойная русская речь. Лексика также немного различается. Например, "лифт" - в американском английском это "elevator", а в британском "lift", "осень" - fall (AE) = autumn (BE), "кино" - cinema (BE) = film/movie (AE), "каникулы" - holiday (BE) = vacation (AE), бензин - petrol (BE) = gasoline (AE), туалет общественный - public toilet (BE) = restroom (AE), мусор (в прямом смысле) - rubbish (BE) = garbage/trash (AE), метро - underground (BE) = subway (AE), расписание - timetable (BE) = schedule (AE) и т.д. Некоторые слова пишутся чуть по разному, например theater=theatre, apologize=apologise, center=centre, honor=honour, color=colour. В британском английском вопрос о наличии чего-либо строится по форме "have you got / has she got..", когда как в американском больше говорят "do you have / does she have...". Всё же думаю, что лучше учить американский вариант английского. Он проще и понятнее. Американцы часто смеются над произносительными особенностями британского английского.

(I speak U.S. English). Wikipedia is a very good place to find answers to this sort of question. Start with http://en.wikipedia.org/wiki/Comparison_of_American_and_British_English A good (if controversial) example of the difference is that the first book in the Harry Potter series is entitled "Harry Potter and the Philosopher's Stone." The U.S. publishers decided to change the title to "Harry Potter and the Sorceror's Stone." This isn't so much a difference in language as in culture. When a U.S. book is republished in the U.K. the British copy editors make dozens of small changes, mostly in vocabulary. "Scotch tape" (a brand so familiar in the U.S. that it is used in ordinary speech as a generic name" became "Cellotape," "Diapers" became "nappies." A funny example of this occurred in a U.K. Penguin edition of John Steinbeck's "The Grapes of Wrath." The dialog is written in U.S. colloquial English of 1939, with occasional misspellings to indicate speech patterns and dialect. So, of course, people do not say "I need to purchase a gallon of gasoline," they say "I need a gallon a gas." In the British edition, they said "I need a gallon a petrol." Blame Noah Webster for some of this. He wrote an extremely popular and influential U.S. school spelling textbook and dictionary. For some reason, he decided to simplify a few spellings here and there, and made just enough changes to be _different_ without being _better_. So U.S. English has a few scattered miserable examples of slightly phonetic spelling, such as "color" instead of "colour." We still have "tough" and "dough" and "thought" (pronounced like "tuff" and "doe" and "thawt") but we spell "plough" as "plow." Webster wanted to go farther than this, and seriously proposed changing the spelling of "women" to "wimmen."