Quad simply means that the skate has 4 wheels, 1 in each corner of the bottom of the skate. Quad skates have always been considered the "traditional" skate and this is what most skaters rent when they go to their local skating rink. Quad Skates are great for those wanting to learn to skate, fitness skate, perform skating tricks, jam (dancing on skates), play roller derby, skate outside, artistic skate (type of dancing on skates), or just those wanting an all-around rink skate.
Inline Skates are very popular skates for those wanting to skate outdoors as well as those wanting to speed skate. Inline Skates feature wheels that are, well, "in line" with each other. Inline Skates have anywhere from 3 to 5 wheels per pair of skate.