The difference between a pig and a hog is all about poundage or weight.
Any swine below 180 pounds is called a pig, and anything above that is called a hog.
That’s in the United States only, though. In England, all swine are considered pigs, whatever their weight.
There are other specialized names for pigs during their various stages of life: a mother sow farrows (gives birth to) piglets; a shoat or weener is a child pig; a half-grown pig is a barrow (male) or gilt (female); adults are boars or stags (male) or sows (female).
Castrated male pigs are also called barrows. What do you call a group of pigs? A wallow.