There are a lot of subtle differences. That being said, they're mutually-intelligible. Even if you don't know the other variety, you can probably figure out just about everything from context.

https://en.wikipedia.org/wiki/Comparison_of_American_and_British_English

EDIT: Even that's not a comprehensive list, though. For example, style guides for American English typically use title case for headlines, where nearly all words are capitalized ("Sinead O’Connor Mourned in Irish Mountain Village Where She Once Lived") and British English style guides typically use sentence case ("Sadiq Khan wins high court battle over London Ulez extension"), though that's really a matter of style and not an absolute divide between the two.

Or how the British usually use "River" first ("the River Thames") and the Americans "River" second ("the Mississippi River") in names.