"Buying" seems to be a term that is used more in merchandise retailing (stores have buyers who buy merchandise for the store to sell at retail). "Purchasing" is the same function (buying from suppliers who typically are external) but is perhaps more formal and more common outside of the retail sector (companies that buy inputs for manufacturing or furnishings and equipment for their businesses have "purchasing departments"). Yet another option is "procurment" but this tends to be more common in government and military organizations.

Now, when talking about consumers, they are usually buyers who buy when they the goods and services bought are commodity, bulk or mass-market items. They are purchasers who purchase when the item is a luxury item or perceived as one. You might buy a Kia but purchase a Lexus, buy Thunderbird but purchase Veuve Cliquot, buy the World News but purchase the Financial Times. Likewise, in marketing materials, customers tend to buy and clients tend to purchase.

I hope this helps.