The difference between butterscotch and caramel essentially comes down to the type of sugar that is used in making each of them. Butterscotch is typically made by melting butter in a hot pan and adding brown sugar, cooking it until it reaches the proper temperature. Caramel is made in much the same way, except plain white sugar is used and sometimes it is melted first, before butter is added to it and then cooked. Both butterscotch and caramel can be used to make a sauce through the addition of cream, and each can be used to make candy.
Butterscotch and caramel are made in very similar ways, though there are some important differences in the ingredients and handling of each of them. The preparation of butterscotch begins with butter and brown sugar. Different recipes may call for various amounts of each, though equal amounts of butter and brown sugar can be used effectively. This is then heated in a pan until it melts down and becomes the proper consistency, at which point it can be used to make hard candy.
While both butterscotch and caramel use butter and sugar, caramel is made from white sugar rather than brown. Brown sugar is basically white sugar that is added to molasses and then allowed to dry out, which is why it has a different color and flavor and is moister in texture. Recipes for caramel may require that white sugar is melted alone in the bottom of a pan, and then butter is added to it and allowed to melt. This is then cooked until it becomes golden brown in color and can be used to make soft candy.
Additionally, both butterscotch and caramel can be used to make a sauce, rather than a solid candy. This is typically done by preparing each type of treat and adding in some heavy cream, stirring and beating the mixture rapidly with a whisk. The addition of cream prevents the sauces from hardening into candy, and instead they remain thick, but liquid. Since caramel uses sugar in general, and butterscotch requires brown sugar specifically, some people consider butterscotch to simply be a particular type of caramel.
Vanilla extract or other flavored oils can be added to both butterscotch and caramel to introduce additional flavor to them. The differences in the sugars used require that each of them be cooked to a different temperature. This is why the hardened candy versions of these two treats are different in texture. Butterscotch is allowed to come to a soft crack stage, a term used in candy-making, while caramel is only cooked to a firm ball stage.