There are two forms to express possession in English. Have or Have got
Do you have a car?
Have you got a car?
He hasn't got any friends.
He doesn't have any friends.
She has a beautiful new home.
She's got a beautiful new home.
While both forms are correct (and accepted in both British and American English), have got (have you got, he hasn't got, etc.) is generally the preferred form in British English while most speakers of American English employ the have (do you have, he doesn't have etc.)
The Verb Get
The past participle of the verb get is gotten in American English. Example He's gotten much better at playing tennis. British English - He's got much better at playing tennis.
Probably the major differences between British and American English lies in the choice of vocabulary. Some words mean different things in the two varieties for example:
Mean: (American English - angry, bad humored, British English - not generous, tight fisted)
Rubber: (American English - condom, British English - tool used to erase pencil markings)
There are many more examples (too many for me to list here). If there is a difference in usage, your dictionary will note the different meanings in its definition of the term. Many vocabulary items are also used in one form and not in the other. One of the best examples of this is the terminology used for automobiles.
· American English - hood
British English - bonnet
· American English - trunk
British English - boot
· American English - truck
British English - lorry
Once again, your dictionary should list whether the term is used in British English or American English.
For a more complete list of the vocabulary differences between British and American English use this British vs. American English vocabulary tool.