It is a Mossberg 500. However, parts only interchange with a model 500 from the same serial sequence, i.e. if you have a G, H, or J serial number, it will only interchange with an older G, H, or J serial number.
Source: National Mossberg Collector's Association at www.havlinsales.com
I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
http://www.histandard.info/PDF/Sears%20Shotguns.pdf
sears roebuck and company
Its a Sears branded Mossberg 500.
The value of a Sears and Roebuck 12 gauge shotgun model number 281512651 depends on its condition. This gun in excellent condition is valued between 100.00 and 135.00 as of 2014.
1952 by High Standard for sears& Roebuck
Winchester 1200
$49.95
410 is not a gauge. 410ga
Sears Slug Model 446.511761 is a Mossberg 500. All parts interchange.
http://www.histandard.info/PDF/Sears%20Shotguns.pdf
You would have to list the model number of your shotgun,to identify the maker of your sears and roebuck shotgun,in order to get the correct buttstock.