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According to Larousse, "porc" is the more generic term. If it's domesticated, it's a "cochon", and if it's wild, it's a "sanglier".
It's more common to use the term "porc" for the meat and "cochon" for the live animal, but it's not an absolute rule. "Élever des porcs" and "manger du cochon de lait" are also common expressions.
