The Parson Jack Russell isn't just the "show variety" of Jack Russells.
My daughter was wanting a puppy a few years ago, and to avoid getting some yappin' worthless toy breed, of which I'm SURE my wife would have steered her toward,...I kind of "guided" her into a Jack.
Anyway, from my research at the time,
There were some breeders and clubs that DIDN'T like the direction the Jack Russell was heading. Just like every breed that gets popular in this country, over breeding causes the breed to suffer.
So, the clubs and breeders WENT BACK to the original Jack Russell standards and adhere to them.
As a matter of fact AKC recognizes the Parson Russell Terrier and not the Jack Russell. I THINK the only kennel club that registers plain Jacks Is the Jack Russell Terrier Club of America. JRTCA.
So,In their quest to adhere to the old standards, they also hunt, and hunt test them. If you do a little research, you'll find a lot more hunting Parson Jacks, than plane or "Shorty" Jacks.
Just to be clear, these hunts and hunt tests are where they go in a burrow, or "to ground" for their game. And then I think the handler digs it up.
Now, I'm no expert. I just happened to do a lot of reading about both breeds before we bought Penny. And she's just a Jack Russell. And probably more of a "Shorty Jack".
I take her with me once in a while, but she doesn't have a clue what she's doing. And if a coyote ever did get ahold of her...goodbye Penny.
But...it'd have to catch her first! She's wicked fast!
That's my ¢.02!!