Good looks are visible, of course--or else we wouldn't call them "looks." So, looking at a perfect stranger and declaring that person "beautiful" seems to me obviously to be a judgment about how the person looks. Looks are, however, just one aspect of a person that can be beautiful, and as the old saying goes, that sort of beauty is "only skin deep." Unfortunately, a lot of good-looking people are not very beautiful in any way other than the way they look.
Remember the movie, "A Beautiful Mind"? I think some minds are beautiful, but obviously that judgment can't be about how the minds look--it would seem to be more about how they work. I also think that people can have beautiful characters, or other beautiful traits or qualities.
It seems plausible to think that there might be some beautiful traits or qualities that are really more important or valuable than others, where good looks will be found to be relatively less important than some other characteristics a person has, which are beautiful. Each sort of beauty, then, would be an example of excellence in the relevant comparison area--so a beautiful mind would be a mind that was excellent at doing the best things that minds do (rather than the worst things). Good looks are excellence in visual appearance. Everyone responds to the way things appear--but we also quickly revise our first impressions (if we are intelligent, that is), and good looks are, after all, very superficial as a form of excellence. Excellence of character seems to me to have more "thickness" or lasting value.
The ancient Greeks had a saying that I love: "chalepa ta kala," which means roughly, "beautiful things (ta kala) are difficult." I think this is a valuable insight. Good looks are fairly common. To be truly beautiful, then, is a rare achievement, and the result of achieving what is difficult, such as becoming a person of excellent character or judgment.