Seems like an strange question, since a ground and partial ground fault are both types of short circuits.
A partial ground would probably be a high impedance ground, often one that doesn't pull enough current to activate a protective device (like gfretwell said).
A good example would be high voltage line falling on dry sand. The sand (basically glass) is such a high impedance that the line never trips. That's why you never see a lineman touch a downed wire without grounding it.
