I also recall that Jack Russells can carry a mutation for achrondoplastic dwarfism, aka short legs. Called ‘Puddin Jacks’ when they occur, this is sometimes deliberately bred for, because cuteness. I’m betting that this is a major flaw in the AKC ‘Parson Terrier’ standard, and that’s why you don’t see the Parsons with short legs. Because the original Jacks are not a bred-to-a-standard breed, they are going to vary a lot more.
This is a very good summary of the differences between them, from Quora, by Jeff Dege:
Originally? Nothing. Over time? Everything.
What happened is that the kennel clubs saw the growing popularity of the Jacks, and determined to take control of the breed standard, just as they had for the Border Collie.
AKC Versus the Border Collie
The Jack Russell owners were opposed to this because they correctly saw that it would destroy the essence of what made a Jack a Jack. They feared that the kennel clubs would do to the Jacks what they had done to the Standard Collie - create a dog that had a consistent appearance, but none of the behavioral characteristics that were so important to what a Jack is.
So, there was a lawsuit, and the Jack Russell owners won:
The Jack Russell Terrier experience - Politics and Culture
The end result was that the kennel clubs chose a new name, Parson Russell Terrier. And at the beginning, the two different names referred to dogs from the same gene pool.
But it’s been a number of generation, now, and they’ve begun to diverge, just as the Jack Russell owners knew they would.
The differences:
Parsons have a closed stud book. Jacks do not. Only dogs descended from the initial list can be called Parsons. Any dog that meets the breed standard can be registered as a Jack, regardless of ancestry.
The Parson standard on appearance is narrower. The Jack standard accepts more variation.
The Parson standard is genealogical. Every puppy in a litter of two Parsons is a Parson, and can be registered at birth. The Jack standard is individual. A Jack can only be registered as a Jack after the age of one, and then only if it meets the breed standard.
But most importantly, the Parson standard has no behavioral requirements. Ancestry is all that matters. Parsons are judged in the show ring, strictly on how well their appearance conforms to the breed standard. Jacks are judged in the same way, except that to even enter the most prized competition, the dog must be certified as having successfully hunted at least one of the recognized prey species: Red Fox, Grey Fox, Woodchuck, Raccoon, and Badger.
Working Certificates
So, what it works out to is that at the time of the split, there wasn’t any difference, but over time the Parsons have been bred to conform more closely to a narrow appearance standard, while Jacks have been bred to maintain their working abilities.
The fascinating behavioral aspects of the Jack - the assertiveness, the obsessiveness, the high prey drive, are being lost in the Parson, as they were lost in the Standard Collie, and are being lost in the Border Collie.
They are being retained in the Jack.