The ingredients are basically the same but the ratio differs. Sugar cookies have higher proportion of flour than shortbread, and less butter. Cut-out cookies are sugar cookies. Try my recipe for sugar cookies! A shortbread cookie contains less sugar but has more butter, and is very tender. The dough is often rolled into a log and cut into slices to bake. Try my one of my slice and bake cookies (I have more than 10 recipes!).