There are two kinds of coupons, manufacturers coupons and store coupons. Manufacturers coupons can be used at any store and will say "Manufacturers Coupon" on the top of the coupon. Most of the coupons in the Sunday newspaper circulars and on the printable coupon sites are manufacturers coupons.
Store coupons are specific to the store that issues them and the coupon will say "Store Coupon" with the name of the store on the top of the coupon. Some of the most common places to find store coupons are in the stores' weekly ads, in special brochures found in the store, in store mailings sent to your home, and from the store websites.
The good news is that you can combine store coupons with manufacturers coupons at most grocery store, drugstore and discount store which can dramatically increase your savings. For example, if you print a Target Store coupon from the Target website for $1 off Brand X cereal, and you also have a manufacturers coupon from the Sunday newspaper circular for $1 off Brand X cereal, you can use both of the coupons to get one box of cereal, saving $2 off one box. Using two coupons on one item is referred to as "stacking" coupons.
However, you cannot use two store coupons on one item, and you cannot use two manufacturers coupons on one item.