According to what I read there might be a difference if you live in England.
The British English refer to purses as in coin purses, wallets or pocket books. So it is possible for someone to carry a purse inside their handbag.
The American English reference to purses is synonymous with a handbag. Also American English uses purses or handbags to refer to everything from clutches, satchels, hobos and everything in between.
So if you live in England there is a difference, here in the states, not so much.