Store cards are usually ones that you may use with specific retailers. Examples of such cards include the Target RedCard Credit Card and My Best Buy Credit Card. A regular credit card, on the other hand, is one that you may use with any merchant that accepts payments from the network your card is linked to, be it Visa, Mastercard or American Express.
A co-branded card can serve as a rather effective middle ground. These cards are issued by conventional credit card providers and have tie-ups with various brands. Like store cards, they offer better rewards when you shop with the brand in question, but you also have the freedom to use them elsewhere. The Costco Anywhere Visa Card by Citi qualifies as a good co-branded card.