Better explanation here...This is copied/pasted from the Tile Council of North America:
What is the difference between epoxy grout and mortar and conventional grout and mortar?
We are often asked about epoxy grout and mortar versus conventional grout and mortar.
Epoxy grout (meeting ANSI A118.3) is quite different from cementitious grout and epoxy emulsion grout. Made from epoxy resins and a filler powder, the grout is extremely hard, durable, and nearly stain proof. Often times the bond between tiles is stronger than the tile itself.
You might wonder why this type of grout is not used all the time. First, most installers find it harder to use than cementitious grout. Also, it has a more plastic appearance which, as with all matters of aesthetics, some people like and some don't. Also, it is much more difficult to shape and slope; this can be done easily with cementitious grout and is often needed to transition from one tile to another. It may also slump in the joint hours after the floor is finished because the grout becomes less viscous initially as it heats up and cures. Lastly, it generally takes days longer to cure and must be kept rigorously clean. And it can cost three to eight times as much as cementitious grout.
There are even epoxy grouts on the market impregnated with Teflon that are both stain proof (nearly) and wipe clean incredibly easily.
It is also possible to smooth epoxy grout (with or without Teflon) before it cures in a way that leaves the surface with an extra slick plastic finish to which it is very difficult for dirt to adhere.
These "100% solids" epoxy grouts should not be confused with epoxy emulsion grouts which are a mixture of cement and epoxy resins (ANSI A118.8). Epoxy emulsion grouts are not stain proof and generally will absorb liquids and stains. They are more similar to polymer fortified cementitious grout (ANSI A118.7) but may have better chemical resistance than some polymer fortified grouts.
Epoxy thinsets offer greater bond strength and chemical resistance than polymer modified cementitious thinset. This performance comes at a price as epoxy thinset is much more expensive than regular thinset. Typically, they are only used to bond to difficult substrates or where extraordinary chemical resistance is needed.