Ha! I'm a welfare worker, this one's right up my alley!!
Back in the old days (like, 10 years ago

), food stamps used to come in paper coupon form. They still might in some areas, I'm not certain. Nowadays, food stamp recipients are given an electronic benefit transfer card that works a lot like a DC. Now instead of handing paper coupons to the cashier, they can swipe their EBT card just like a DC. Food stamps can be used to buy, duh, food products. You can't buy things like toothpaste or toilet paper with them.
Some areas might still use the paper coupons, I'm uncertain. We were actually just sent an email a few days ago letting us know that there is currently legislation in the works to decertify all paper coupons (i.e. make them worthless) a year after passing the law. I think this might only be because the paper coupons never expired, and some people still have some. I don't know.
swede96, that sounds a lot like WIC (Women Infants Children). WIC gives recipients X amount of something per month. Generally, it's baby formula that women use them for. I'm not aware of any food stamps that require you to buy certain brands or foods. They can be used on any food.
Cash welfare is handled the same way: the money is placed in the account linked to the EBT card. Unlike food stamp money, cash welfare can be withdrawn at an ATM or used on anything.