The difference between sorbet and sherbet is that sherbets contain milk or another fat, making it similar to ice cream. Generally thought of as being fruit based, sorbets can be made with any ingredient.
Sorbets are technically ices (as in Italian ice) and are also referred to as granitas. They were actually the first iced dessert, probably having been invented by the Asians and then introduced to the Middle East and Italy. They are generally granular in texture where sherbet is creamy as a result of the added fat.
The smoothness of a sorbet is also dependent on the secondary ingredients because of how they can change the structure of the frozen recipe. More or less sugar or alcohol or even the amount of water will make a big difference in the texture of the recipe.