TopGun, the first one you have is the Squadron patch. The second one is the Squadron insignia for the aircraft. Although it's slightly different than the one I'm used to seeing. I think that the insignia that you have is the Squadron's original, and it was changed slightly to the one I've seen. The one I saw was the same tiger, flying (tearing) through a Chinese Air Force insignia, tearing a Japanese flag with it's front claws. I think he had an Uncle Sam hat too, because I remember a U.S. flag reference of some type...
I'm positive about the tearing of the Japanese flag, though. I think that the signifigance of the insignia I described was that the U.S. was striking at the Japanese "through" the Chinese Air Force. Pretty ingenious, actually.