Mordu was the oldest outta all the three Princes from the other kingdom and he was turned into a phantom bear after he let pride, selfishness and anger get the better of him and those three elements have been keeping him alive for many years. And the bear that attacked Merida's father was just a minor character bear pretty much.
the person above me is incorrect. King Fergus literally calls the bear at the beginning Mor'Du. Mor'Du ate Fergus' leg and obviously Fergus was unable to kill him. It is the same bear. He's kept alive by magic. So to answer your question, yes, it is the same bear, but your question is erroneous because Fergus did not kill him.