When you purchase a pair of shoes, you buy them. If you want to gain purchase, or favor, with new friends, you might tell them about your recent purchase of chocolate, and offer to share.
Purchase can refer to the act of buying or the thing you bought. In 1803, the United States paid France approximately $15,000,000 for 800,000 acres of land which was called Louisiana, in a transaction known as the Louisiana Purchase. In this transaction, the purchase nearly doubled the size of the U.S. — the territory purchased comprises about 23 percent of current U.S. land.