Welcome to the site.

The gun you may be thinking of was a couple of years ago, there was a few special run Savages that was offered by one of the Big retailers, (Gander mountain, dicks, etc.) that matches the description you have described.

They was numbered something like a 12bvth, the closes thing to it would be a 12bvss, or a 12vlp.
Yes there is a long and a short action offered in Savages, in factory guns, short action calibers are built on short actions,( 204, 223, 22/250, 243, 308, 7mm08, etc) and long action calibers are built on long actions, ( 25/06, 30/06, 7mm mag, etc) you can not pick unless you build your own.

By looking at your post I am guessing you are wanting a 308, I don't think the special run gun aforementioned came in the caliber, only in 204 ruger, 223, and 22/250. The vlp does not come in 308, and I am not sure the BVSS does anymore.