You can think of American English and British (UK) English as dialects where the words are the same but the SPELLING is different.
You will find people from Australia will usually use UK English with a little bit of US English, while people from Canada will use a combination of US and UK English.
UK English will usually be the one with more vowels (for example UK:Colour/US:Color, Aeroplane/Airplane, Caramel/Carmel) or more double-Ls (for example Traveller/Traveler, or Marvellous/Marvelous).
US English is usually spelled more like the way it sounds (for example US:Capitalize/UK:Capitalise, or Defense/Defence).
This isn't every difference and there will be many confusing exceptions.
Here is a link that might help you: http://www.tysto.com/uk-us-spelling-list.html