They have different accents, a very small amount of words are spelled differently, but grammatically they're identical. Non-native speakers tend to exaggerate the differences between the different English accents. If you can understand one accent, you will be able to understand all the others without any problems.

The differences are small. There is only one language. There are regional differences in English within the U.S.. There are regional difference in English within Great Britain. The differences between the U.S. and Great Britain are just another regional difference. For historical reasons we use different dictionaries. Here are some common words. By noticing which words you've learned you can tell whether you've learned British or U.S. English. In each case I'll list British first, then U.S. "Today, the sky is a beautiful blue colour/color." (A difference only in spelling, not pronunciation). "I walked into the skyscraper and took the lift/elevator to the fiftieth floor." "The country has a good system of railways/railroads." "I haven't studied maths/math since high school." "I just filled my car with forty litres of petrol/ten gallons of gas."

Sometimes the pronunciation is a little different, and some of the vocabulary is also different (elevator/lift, trunk/boot, on vacation/on holiday). The slang is definitely different. You'll be understood, though, if you're not using slang so don't worry about it too much.

American and British English are not grammatically identical. Nor are the differences between the two "regional differences." GB is not a region of the US or vice-versa. There is a lot of material out there to help you see the differences. Good luck, Zelina!