Large shank short action could either be precision target action, single shot avilabile in a variety of bort/eject options (silver), or LRP based repeater actions (black).
In long action, there were some RUM based 110 (maybe 112) based large shank actions that were just standard actions. Don't see the standard large shank actions much as they were not used for very long. I have been wanting one for a long time, just because I don't have one yet, and haven't seen one up for sale in a long, long, time. There is also the 112 target magnum, which I have a few of (switched a lot of short action PTAs to these actions), which come in 338 lapua. But it is a long action large shank action with target accu-trigger. Can fit about any round, within reason, into it. I have used these for 6BR up to 338 Lapua AI.
Another consideration with the short action precision target actions is bolt spacing. There are 4.4" spaced actions, but also "palma" target actions which are like 3.44" bolt spacing.
I have used quite a few versions of the single shot target actions and have been extremely happy with all of them, as well with the 112 target magnum actions. I have a LRP repeater action sitting in my safe now waiting on me to decide on what to do with it, so can't speak from person usage, but do have a group of shooting buddies that have about 8 LRPs between them and all love them.
Good luck with your search.
Ben