"Face on a face" can be considered a couple of ways. On the surface, the clown is funny and lighthearted but often this signifies a deeper meaning.
A hidden face is an attempt to hide from reality. Something might have happened that causes a person to hide or attempt to cover up an action. You might think about a recent situation that was scary and you wanted to hide.
Or maybe you don't want to be associated with something??? Very subtle meaning in many cases.
And of course, the first meaning can just be that of fun. Nothing more serious!