There is no difference in meaning, and - once again - it's a question of formality. British English uses the word 'purchase' even less than American English does, and it would sound odd to use the word in everyday conversation.
You would never comment to a friend, for example, that you had 'purchased' something - you'd always say 'bought' or the all-purpose 'got'. However, if you were writing a letter of complaint to a company about a faulty product, it would be appropriate to use 'purchase'.
By the way, the noun 'a purchase' is quite useful, as there isn't an equivalent noun from the verb 'to buy'.