Parson Jacks and Jacks are different. I'm not sure if the Kennel Club has yet recognised either as breeding true.

Most things sold as Jacks are small short-haired terrier mongrels. I have a friend, much into pikey (justified in this case) dog breeders, from whom he got two Jacks - an alleged "mini-Jack", probably a Jackx2-Chihuahua-whippet cross - tiny with bat-ears, ran like the wind for her size and yapped a lot - and a "Bull-Jack" which was a bit like a smaller Staffordshire Bull Terrier - about twice the width of a Jack, and jaws like a mechanical digger. Turned my Great Dane over twice, before the day she got him in her mouth from end-to-end (yep, head to tail, not across his back) after which he showed more respect. Allegedly his sire was "The Rat" well known on the Essex dog fighting scene. The dog was taken into the local pub (now shut) once. A local travelling boy (hard as nails, ex 2-para) said "What the fuck is that? Good fighting dog. I know fighting dogs, let me see." He got bitten, the landords LabX got turned over, Bosun shat on the carpet, pissed on three table-legs, and left in disgrace. Both had to be rehomed.