Sherbet is a lower-fat, fruit flavored and more dense alternative to ice cream. It is made with 1-2 percent milkfat (any less and it would be flavored ice and any more and it would technically be ice cream). Ice cream is fluffier, because as it is being made/churned, air is incorporated into it, while sherbet has very little air. Less air means sherbet is also generally more intensely flavorful.
Recipe: Refreshing Lime Sherbet