What's the difference between a white hole and a wormhole?

A white hole is the theoretical exit of a black hole. If, once you reach the singularity in a black hole perhaps there is an exit. That exit would be the white hole. A wormhole is the shortening between two points of space by manipulating the very fabric of space by traveling so fast it warps.

Both are theoretical. The white hole should be an area of space into which the energy from a black hole is expelled. This would be accomplished via a wormhole or some other breach of space. Hawking expects that there will be a form of radiation of dark energy, oddly enough termed Hawking Radiation, that will be emitted from a black hole and that no wormhole or resulting white hole is required to achieve a balance of forces. My personal theory varies substantially from each of these but embraces both.

White hole and worm hole are both explanations to black holes. Worm hole is a possibility of black hole linking to somewhere through bent space while white hole is a possible worm hole.