If your budgie's claw has been damaged to the point where it is purple or black, the claw is now dead tissue, and should be removed expertly by a vet. If it stays there, the whole foot could become infected. More damage could also occur as the bird has no sense of feeling in that claw, and anther knock or tear could extend further up the foot.
Razor claw or quick claw.
beak
The claw of an eagle, hawk or any bird of prey is called a talon.
Claws or Talons, depending on the bird
Bird claw
Talon
its a talon
talon
The Southern cassowary of Australia has a claw for its middle toe.
Talon Talon
While we don't know about your bird's history, health, or living conditions, many birds (as well as other species) will playfully nip at another of their species. In general, this behavior is about establishing dominance, although it can also be a sign of insecurity. Under normal circumstances, it doesn't hurt the other bird, and it shouldn't draw blood. If you find the behavior unpleasant, feel free to use positive reinforcement to teach the bird not to do it; if the bird is biting at you, it is especially important that you set boundaries, rewarding the bird for appropriate behavior. Of course, if your bird is going beyond occasionally nipping and instead trying to claw or injure, then that is not normal behavior for a budgie (parakeet), and you should probably consult your veterinarian to discuss what might be causing it.
talon