The easiest of these to define is the shortbread cookie like the ones in these Linzer cookies. Shortbread cookies should be crisp and tender and a bit crumbly, since they are made without egg. Compared to the 1-2-3 baking ratio of sugar, butter, and flour in shortbread, these sugar cookies have more sugar and butter as well as the egg. Lots of people have an opinion, but there doesn't appear to be a clear definition of what makes a sugar cookie versus a butter cookie.