The "inbetweener" as you call it is more accurately called the Gen 1 short-actions that were made from 1958-1988. These Gen 1 actions are approximately 0.540" shorter than the standard long-action receivers. It wasn't until 1998 that Savage finally came out with a "replacement" short-action, the Gen 2, which was 0.850" shorter than the standard long-action or 0.310" shorter than the Gen 1 short-action, with an action screw spacing of 4.275". The current Gen 3 short-actions have the same overall length as the Gen 2 actions, but have a slightly longer 4.40" action screw spacing to accommodate the newer detachable box magazine and hinged-floorplate magazine bottom plate designs.

As Dave finally noted, the "J-Series" has nothing to do with the action length or screw spacing, but rather is a part revision indicator used by Savage to know which version of a given part or parts should be used if the rifle ever comes back to them for repair. At this point the "Series" indicator is meaningless as none of those various revisions of the parts have been made for several decades and nobody knows what the small changes were anyway.

If you want some detailed reading on the history of the 110-series rifles, I recommend reading the five articles linked to below. To of them were written by Robert "Bob" Greenleaf for the now defunct "Precision Shooter" magazine. Bob was an engineer at Savage Arms from 1964 - 1988 when he was forced into retirement due to company going into bankruptcy protection, but continued to do consulting and testing work for Savage on a contractual basis into the mid 2010's. Sadly Bob left us in the summer of 2017 at the age of 94.

https://www.savageshooters.com/conte...?294-model-110