A stray is a cat who has been abandoned or who has strayed from home and become lost. Stray cats can usually be re-socialized and adopted.
A feral cat is in unsocialized cat. Either he was born outside and never lived with humans, or he/she is a house cat who has strayed from home and overtime has thrown off the effects of the domestication and reverted to a wild state.
Feral cats should not be taken to a local shelter to be adopted. Feral cats are not pet cats, and they will be killed at most shelters. Because they are un-adoptable, they sometimes don’t even make it to the shelter, but are killed in the animal control truck. Even no-kill shelters are not able to place feral cats.