The english accent and the american accent are so different?

i studied English at school and often my teacher(or professor?)says something like:"english speaks in this way","americans in that way",and for me it's very difficult to understand the difference...for me it's the same thing!and when i listen james blunt or justin timberlake i don't hear the difference...but about robbie williams?he's english and how speaks him?and when you watch english films like harry potter...isn't strange for you?and titanic...rose was english and jack american...it wasn't strange hear 2 different accents?