Oh, you know not what you ask! This is major doggy politics, or it was back in the 1980s.
No, not " dwarfism," but probably more Sealyham terrier way, way back in the line. "Puddin" is a pejorative term -- what you have is a Jack Russell Terrier with short legs bred to be a working dog primarily. I'm not aware of any major joint problems with JRTs, but if I were buying one I'd definitely ask the breeder about it. They are great little dogs with masses of energy.
I'll try to keep this short! A so-called "puddin" is probably closer to the original version of the terrier bred by and named after Parson Jack Russell back in the 1880s. It was probably a mix of Fox Hound, Sealyham and other terriers. The short legs were deliberate so it could "go to earth" (go down holes) after animals more easily during a hunt. As a working dog, there was a lot of variation in the breed standard.
These days people are more familiar with the long legged almost all white
Parson Russell Terrier. This is a variant of the Jack Russell Terrier and has to do with breeding to a different set of breed standards in order to get AKC recognition. This standard had longer legs and less color, thus the Parson today is prone to eye problems and deafness.
The change in standards caused a major rift between the Jack Russell Terrier Club of America and the Jack Russell Terrier Breeders Association (JRTBA) as the those who loved the shorter legged terriers wanted to preserve the "working" terrier and not breed more effete (in their opinions) show dogs. The debate got very testy and finally forced a name change for the "variant." I was a member of the JRTBA back then and remember the fights.
I owned a JRT from 1986 - 2004, yes she lived to 18. She was born a JRT and remained a JRT, although she would probably have fit the breed standard for a Parson Russell due to her long legs. She was also one of the best dogs I ever owned.