Common Vocabulary Differences in British and American English
For example, if you say to a British person "I like your pants," they might be surprised that you are commenting on their underwear as they say 'trousers.' If someone describes a person as 'mean' in British English, it means someone who is not very generous. In American english it means nasty. If you ask for a rubber in the UK, it's used for erasing pencil marks, but in America this is contraception, so be careful!
More Vocabulary Differences in British and American English
Car parts are quite different. The British put their bags in the 'boot' of the car and the Americans, the 'trunk.' Food terms are quite different. For example the British eat a pack of 'crisps' and the Americans, a pack of 'chips.' We order a portion of 'chips,' and they order a portion of 'French fries.' British babies suck 'dummies,' and American babies, 'pacifiers.' The British put out their 'dustbin,' and the Americans put out their 'garbage can.'