Fat Skin VS Thin Skin

I noticed that some people have thicker skin than others.

For example, I’m not fat, and at some point (when I was a (bad) competitive swimmer) I was downright too skinny. However, when we had those fat tests (with the thing that pinches your skin at different places) I was always among the ones with the highest fat content. Now that I swiched to Kung Fu, I notice that my fat skin has the advantage of not cutting that much around the nuckles (since we don’t hit each other in the face too much my only experience is with the nuckles but I’d assume it to be the same all around). Whereas some people constantly have plasters around the nuckles, I never need any; in a year I think I cut myself only once or twice.

So, what gives? Is skin fatness and skin thickness the same thing? Is it that for some people the fat doesn’t stick under the skin (so you can pinch only the skin instead of pinching skin+fat). Is one better than the other? Am I suffereing from desillusions and need to have a better look in the mirror?

And another thing, why is it that some people have hard fat and others soft fat?