There are a few simple differences between shortbread and sugar cookies and also a slight difference in taste. Most of the variances have to do with texture, ingredients and traditional decorations.
Sugar cookies often have many ingredients, including eggs, vanilla, salt and a leavening agent such as baking powder or baking soda. Traditional shortbread has four ingredients at most: sugar, butter, flour and sometimes vanilla.
Shortbread and sugar cookies are often chilled and then rolled and cut with cookie cutters, but sugar cookies can also be made in the style of a drop cookie without being rolled out.
Texture and Taste
Shortbread is almost always thicker and denser than a sugar cookie. It contains more butter than sugar cookies as well, so the taste is richer.
Baking times don't differ much, but shortbread is often baked longer than sugar cookies by 2 to 5 minutes.
Though shortbread is most often eaten plain and left undecorated because of its rich flavor, bakers tend to frost and decorate sugar cookies with sprinkles or granulated sugar.