Welcome to the Forum. The 44 American and the 44 Russian, 1st Model started with serial number 1, so a serial number in the 11,XXX range could be either. Check the cylinder chamber and if smooth, it is an Amercan and if it has a step in the chamber, it is a 44 Russian.
Ed has much more knowledge on these era guns than I do, but I have not seen such strong prices realized for some time. This is only a guess based on auction observations from many gun auctions over the past couple years. I used to have several 44 S&W top-breaks so am always interested in what auctions prices have been realized.
I have seen prices in the $2500 range for the big 44 Hoglegs with little original finish left and worn stocks like yours. I typically see prices under $1000 for Baby Russians in decent condition, but the finish looks to be mostly intact on your 38 Single Action, 1st Model, so $1200 - $1500 max for me is possible. Bottom line is that the person who offered you $1600 for both is a thief. Even if it was a purchase for resale, it is no where near a fair offer using value estimates of either $3800 or $5000!
BTW, the pictures are very helpful, but you can up to 5 images in a single post by using the same process, just keep adding images in the same Manage Attachments window until five are attached and then post.