J. Stevens Arms was bought by Savage Arms
in 1920. I believe they continued a line of Stevens shotguns for a while after the acquisition.
I'm afraid I can't offer much more than that, but there's a forum that specializes in shotguns, the Shotgun World
forum, that might be able to provide some information for you.
You ask "what they'd generally be used for." The answer to that is self-defense and tactical situations. Then and now, people saw off the barrel (and often also the stock) to make the gun smaller and easier to maneuver (and also easier for gangsters to hide under their trench coats).
Good luck in your search.