English is such a peculiar language.
It's pretty interesting actually.
Cow, Pig, Sheep, Chicken are all Anglo-Saxon (Old English) derived words.
However, after England was conquered in 1066 by the Normans, we gained a lot of 'Old French' words.
There was also a shift in power/class systems, and for the most part Normans were on top (Lords, nobles, etc.) and Anglo-Saxons were on the bottom (peasantry, farmers, etc.).
As a result it would be the Saxons who were farming all the meat, which is expensive, and the Normans would be eating it.
When the animal was alive it was around Anglo-Saxons and had their name for the animal.
When the animal was dead it was on a Normans table and had their name for the animal.
Hence we have livestock like;
Cow, Sheep, Pig and Chicken.
And we have meat like;
Beef, Mutton, Pork and Poultry.