My take on the different Jack Russells:
Parson Jack Russells, Jack Russells and Russell Terriers are all often advertised as "Jack Russells" in newspaper and magazine ads. We advertise our Russell Terriers as Jack Russells; as most people don't know that the cute shorty jack russell terrier is now known as the AKC Russell Terrier. Parsons get advertised as Parsons but sometimes, even they, are advertised as Jacks! Clear as mud, right?
The Parson Russell Terriers are built square and 12 to 15 inches as recognized by AKC. In UKC conformation shows, there are also Parson Russell Terriers, and they are divided into two size classes: 10 inches to 12½ inches, and over 12½ inches to 15 inches.
The Jack Russell Terrier Club of America's (JRTCA) dogs are 10 to 15 inches. The club does not currently support AKC or UKC recognition and the JRTCA very successfully, does all their own shows and events.
Then there are the Russell Terriers, They are the short legged ones. Because of JRTCA using the Jack Russell name, the AKC decided to call them Russell Terriers. They are 10 to 12 inches and slightly longer than tall... rectangular in shape. Russell terriers were just recently added to the AKC FSS program, but we are not yet allowed to show at AKC shows. So any you see at the AKC conformation rings are Parsons, not Russells. Beginning January 1st, 2007, Russell terriers were allowed to perform and title in AKC performance events such as agility, obedience, and rally. I have already title Tee and Patchy in Rally. Meatball and Gunny have titled in Rally Excellent.
As you can see, it is very confusing to try and explain. I have only had this breed since 2004 and I may not have it all right, but I think that you can have a JRTCA dog and register it as a Parson Russell or Jack Russell in the UKC, not sure about open registration for Parsons in the AKC but Russells are still open for registration. I think that JRTCA may not register your dog if you have AKC or UKC papers. Mostly to register you need a three generation pedigree, pictures, and for your dog to conform to the standard.
My Russells are registered as Russell Terriers with UKC, FSS AKC & with EJRTCA.