In PRK the epithelium (top layer of the cornea) is scraped off and then the laser treatment is applied. A contact lens is used as a "bandage" to decrease discomfort. The epithelium then grows back over the bare area during the next few days.
In LASEK the epithelium is exposed to 20% alcohol which helps separate epithelium from the cornea. The epithelium is pushed to one side and laser treatment applied. The epithelial layer is replaced back onto the eye and held in place with a contact lens. The contact lens is then removed a few days later. LASEK is hence a "no knife"/flap operation.
Epi-Lasik is a similar procedure that uses a keratome like that used for Lasik, but engineered to only separate the epithelium. The epithelium is left on a hinge, laser treatment applied and flap replaced.