What kind of guitar has a figure-8-shaped guitar case? What kind of guitar is it if it's not a rule in the upper right corner? Thanks for the advice.

The figure-8 shape you are talking about is a rounded corner guitar, and the missing piece is a cutaway guitar. The main reason is that cutaway guitars make it easier to play close to the back end, as there is one less piece of hand to push through easily.

In terms of timbre, some people say that rounded horns will have better timbre. In fact, this is a theoretical statement. Generally speaking, there is not much difference.