Welcome to the Forum. Your gun is a .38 Double Action, probably a very early one, judging from the grips if they are original to the gun. If you can supply the serial number and verify that the same number is stamped on the butt, on the back side of the right grip panel, on the back of the barrel between the "ears" and on the back of the cylinder, and on the bottom of the barrel latch, we can give you better info. on the gun. Ed.
Apparently this is a Third Issue or variation of the .38 DA series. The serial number is needed to ascertain which type it is. If you want; use x's like: 356xxx to get us in the ballpark.
As to your revolver there are a few things that I've noticed. One is that the hammer has been bobbed (spur used to cock the revolver removed) and the barrel hinge pin (photo #2) is not "clocked" properly and sits proud of the hinge. There are 'witness' marks that should align at the hinge. Back the screw out three turns and tap the screw head which will drive the opposite side pin out slightly. Turn the pin to align the witness marks and tap the pin in and tighten the screw on the opposite side. Done.
Top break 38sw ctg
Linear Mode
