Both nations have very similar grammar, and the spelling is almost always the same. Some words are written only somewhat differently.
For example, in America, they write “color, C-0-L-O-R”, while in the United Kingdom, the spelling is “C-0-L-O-U-R”.
Even if there are differences in the written language, the differences in the spoken language are much easier to spot. You are certainly going to be able to hear that there is a difference when they speak.
So, can you hear the difference between an American and British accent?
If you are curious to test yourself, you can take a look at this interesting video that will show you some of the differences between American and British English!