I can't find either of those models in my cross-reference list. Closest is .5350 or .5380. Both of these are the Savage model 18. I don't know the production years for this model, but a bolt-action is unlikely to have been made before the 1920's and could still be in production.
your sears shotgun was made by savage arms.There model number was savage model 96.
I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
No sn provided and there is no sn data for Sears.
Winchester
Your local gunsmith may be able to clarify whether or not Winchester actually manufactured that shotgun for Sears.
Stevens
Winchester
Winchester 1200
about $100
The Sears Roebuck Model 300 12-gauge shotgun with serial number 273521160 was manufactured in 1964. This shotgun was produced by the High Standard Manufacturing Company for Sears, Roebuck and Co. It is part of a series of firearms sold under the Sears brand during that era.
Winchester, same as model 1400.
Your 12 g pump shotgun was made for Sears by the High Standard Company- it was their Flite King model shotgun.