As far as I understand, the Hebrew culture eats Kosher and those animals that are kosher have another name for when they are being eaten as foods. Thus,
Chicken (food) = עוף Chicken or rooster (as a living animal)= תרנגול
Beef (food) = בקר Cow = פרה
But pig would not be eaten as food so pig and pork are the same word i.e. חזיר.
But I am no native speaker, this is just an observation that I made. Please correct me if I am wrong.
Nice guess, you can half-add כבש (mutton) vs. כבשה (sheep). In this and in your example the meat name is also the living animal name, but not the word commonly used, or more general, or some other difference.
But check out אווז, ברווז, עגל, טלה and דג - all kosher, all used for the meat and the living animal alike.