The liver of fattened geese is foie gras, rich and buttery, seared in thick slices or made into pâté on Western menus; China is now a large producer. Chaoshan cooks also braise goose liver in spiced soy stock.
On Chinese menus, 鹅肝 almost always means French-style fattened goose liver (foie gras), a staple of high-end Western and fusion restaurants since the 1990s. For ordinary cooked goose liver in a Chinese context, you'll see 卤鹅肝 or just 鹅肝片.