As both a noun and a verb, scuffle involves an all-out brawl. As a noun, it is the clash itself, like a scuffle between sworn enemies, or as a verb, it refers to the actual fighting, like a bully who will scuffle with just about anyone.
A scuffle is not an organized bout: it is a free-for-all, with fists flying in any and all directions. As a verb, it tells about the act of this kind of wild fighting, like angry kids who scuffle to try to settle their problems, but it can also mean "dragging one's feet while walking." Here, the meaning is not related to fighting, but rather the sound made by those shuffling feet.