Two names travel together on the regional PAT list: Coniglio in umido and Coniglio alla cacciatora. Both point to rabbit given time in the pot, not a flash in a pan. The grouping itself is a clue that this is one family of slow, sauced cooking rather than two unrelated dishes competing for attention.
The regional method is unhurried. Aromatic herbs perfume the meat as it cooks down with wine and tomato, so the sauce thickens around the rabbit instead of sitting apart from it. You can almost hear the simmer: wine lifting the richness, tomato giving acidity and colour, herbs keeping the whole thing savoury rather than heavy.
If you meet either name on a menu or in a register, read them as paired traditional preparations of the same idea: rabbit cooked slowly with herbs, wine and tomato. That pairing on the PAT list is the useful orientation—look for the long simmer, not for a separate technique under each title.