The major difference between the 37 and the 37A is that the hammer and break lever position on the action are reversed. On the 37 the hammer is behind the lever and on the 37A it is vice versa.
I owned a new 37 in 16 gauge when I was growing up. I traded in my Stevens .410 and 16 dollars for the Winchester at the Western Auto store in Thompson Falls Mt, more years than I care to recall. My paper route paid me $30 a month and I thought I was flush. It was a good beginners gun. I bought one in 20 gauge for my son just last year and we were going to revamp it. A custom gunmaker friend, Maurice Ottmar, took one and added a rib, put on a straight stock of English walnut, had an engraver intall a gold border line around the action and then had Doug Turnbull color case the receive. Maurice rust blued the barrel. The break lever was peirced and reshaped to create a three dimensional scroll leaf for rhe lever. It was to say the least, phenominal. He sold it through Morris Hallowell (www.hallowellco.com
) for $4,000.
The 37's and 37A's are of course not in the price range. A 100% 37 will bring over $300 though with the 37A's being about half of the prices on the 37. There were some factory 37's that had a rib and I did see one and the asking price was $900. I thought that it had to be a special order gun but was told by someone who knew them backward and forward that it was offered that way for a brief time.
My project got sidelined for my son when we found him a new O/U that although will not look as classic, it will function better for him. My projects seem to take too long to get to completion anyway. Too many stumbling blocks like making a living, customers and other boring things. My 37 is for sale, if you are interested, for what I paid for it at $150. Bore is like new, wood is 70 to 80% with no major dings and the metal is 65% with some bare spots but no pits or rust.