The accents of between AmE and BrE are just one of many things that are different between them. Americans use words Brits don't, Brits use word Americans don't (e.g. trainer = sneaker, nappy = diaper and 1st floor in America is ground floor in Britain). For a list of such differences, go here: American and British English differences - Wikipedia, the free encyclopedia
Where you have different places where language is spoken, you will get a divergence of dialects.
As George Bernard Shaw said; "Britain and America are two countries separated by the same language".
[Not a teacher]