To buy is to purchase; to purchase is to buy. They mean the same thing. You can buy a loaf of bread, a car, a plane ticket, a house, a farm, a company, a ship, a fleet of jet planes. You can also purchase these things. The word purchase is more formal and is more likely to be found in business, legal and financial documents such as real estate literature, contracts, accounts, etc.
It is very bad manners to correct someone in that way, even if a mistake has been made. You could try asking your girlfriend why she chose to attack you in that way. You could consider whether someone else might be kinder to you.