Is the clown in Batman Jack or a clown?

The clown in Batman 1 is famous for his surname Jack Napier.

The clown in The Dark Knight is a mystery. Police officer Gordon said that the clown "doesn't match his fingerprints, DNA and dental records, but he is wearing a costume, with only a knife and bandage in his pocket, no name and no other identification", and he finally didn't know the clown's past identity.

JOKER is a ghost card in poker, and the clown in English is JOKER.

These two films are directed by two directors, which are two different series and have no connection with each other, so the plot and character setting are different.