What's the difference between gelcoat with wax and without wax?

Gelcoat is available with or without wax. To cure properly and completely, gelcoat needs to be devoid of oxygen.  

Gelcoat with wax has had paraffin wax added to it. When the gelcoat is catalyzed with MEKP, the wax rises to the surface throughout the cure, keeps the air from contacting the gelcoat, and allows the gelcoat to fully cure. If catalyzed with MEKP, gelcoat with wax will cure completely, in normal application conditions.

Gelcoat without wax is used when you have a different method selected to cure it. Gelcoat without wax is commonly used for laminating gelcoat in stages, or when applied onto a waxed mold, where fiberglass (or another reinforcing fabric) saturated in polyester resin is laminated onto the unwaxed gelcoat. Other products such as PVA (polyvinyl alcohol) can also be applied over gelcoat without wax to cure it. PVA is commonly applied by brush or spraying.

Gelcoat without wax, or any other air dry product that has been catalyzed with MEKP, will generally harden, but remain sticky. More gelcoat or polyester resin can be applied directly over this and still form a chemical bond while it still has a tacky feel. All of this material will remain tacky until it is no longer in contact with the air.