If I remember correctly from baking both Shortbread and Sugar cookies. They have the same ingredients, just that the sugar cookies have more sugar in them so they're sweeter.
Also I love your pine-ception on the tree cookies, Piney. 
Actually, if you want to be persnickety, "shortbread" dough is only moistened with butter (or sometimes substitutes such as margarine or shortening, like in the folksong
"Shortnin' Bread"), producing a dense, rich, crumbly cookie.
Sugar cookies (and most other American cookies, like chocolate chip) typically include eggs as well as butter, and leavening such as baking soda and/or baking powder, which makes the cookies lighter and crisper than shortbread. The protein in the eggs gives the cookies more tensile strength so they're less crumbly and the dough is better suited to rolling out and cutting into fancy shapes.
