Gotta love that Chain Damascus pattern on those barrels!!
I believe one needs to push that button to remove the barrels from the frame. While all of these shotguns I've got pictures of are engraved "FOREHAND ARMS CO." on the top-lever, 1129 and 1170 have the F&W in a diamond stamp of Forehand & Wadsworth on the watertable.
Of the guns I've recorded, those in the 1xxx range have three pins through the frame --
1129 09.jpeg
and those in the 3xxx range have a single screw on each side of the frame --
3296 06.jpg