One grows a pig, not a pork. Once you kill the pig, its name is supposed to change to pork, though why, I never understood quote well.
Because the English upper classes were speaking Norman many of the culinary terms such as pork, beef, and poultry in modern English come from the Norman language.
But because animals would have been raised by common people they retained the Old English derived names such as pig, cow, chicken.
Cow/beef
Sheep/mutton
Chicken/poultry
https://ell.stackexchange.com/questions/32560/why-are-beef-a...