There are many differences between American and British English, but don’t stress too much, just change your Microsoft Word to British spelling (some professors don’t care if you use American English as long as you keep it consistent) and get used to hearing words in unfamiliar contexts.
Below are some of the differences in semantics I’ve come across in Edinburgh:
course = course and class, but also program
mark = mark, but also grade
college = high school
interval = interval, but also intermission
rubbish (bin) = garbage (can)
brilliant = awesome, cool, amazing, etc.
knackered = tired
cheers = cheers, but also thank you and goodbye
suss out = check out
curriculum vitae = curriculum, resume