A friend of mine pointed out recently that a terrier is so called simply because it chases animals into the burrows in the earth or terre (or terrain). It is an earth dog - in roughly the same way that poodles were once pudelhunds in German, or water dogs, or in English puddle-hounds.
If you have two terriers bred for fighting that can be pitted against each other, they are pit-bull terriers. And there really was a Jack Russell. He was a parson who, while at university, bought a white terrier with dark tips to its ears from a milkman.
A terrier's feet are, etymologically, subterranean.