The difference is that "Seminole" is the actual name of a people, whereas "Redskins" is just an outdated, non-PC blanket term for all American Indians/native Americans/etc. There's no Redskin tribe, you know? It's like "orientals." If there was an NFL team called the Orientals, people would flip out.
I'm not saying I'm staunchly against the Redskins name—so don't flip out on me, NS. I don't really know where I stand on the whole thing.