There is quite a bit of overlap between the two. But here is the gist .. A sculpture is generic term for an object that is the end result of a specific process - sculpting in this case. A statue is an object made in the likeness of a person/deity (most commonly) and can be made using sculpting or any other means (e.g. molding).

The difference is a bit subtle. A statue is a representation of a person or an animal but a sculpture is probably most associated as being a piece of art and may or may not be a person or animal.