The one circled in blue is not a Model 34. There is no adjustable rear sight and it lacks the shark fin front sight.
It would help if you had the serial number. Also, is it a .22? Maybe a .32 HE. That would allow a 3 1/4" barrel.
I think it might be an I frame and the extractor rod appears to be barrel shaped, which would lead one to believe it is from before 1947. Unless the picture is misleading. The stocks are post-WWII.
Edit: I see Gil snuck in before me (no adjustable sight).
It's a five shot J frame round butt so a Model 32 .38 S&W or a model 36 .38 Spl made between 1966 when the flat latch ended and mid 1968 when the diamond around the grip screw ended.