After reading this I got curious . I have a 38 S&W that came with a box of Winchester ammo.
Tried them out in an old Colt Police Positive Special (38 special), a S&W model 637 (J- frame 38 special), a S&W model 66 (k- frame 38 special) and a three screw Ruger Blackhawk (357 magnum).
Surprisingly , the 38 S&W would not fully chamber in any of them. The old Colt Police Positive Special (circa 1923) came closest, about 3/16 inch of case would not seat. All the other's left about 1/2 inch of case sticking out.
I pushed on one, in the Colt, just a little to see if it would easily seat but it didn't want to go in any deeper, and then it didn't want to come out either , had to use fingernails to remove it so I didn't "push" the issue any further .
If you have a 38 special that will chamber them, it may be an old 38 S&W that has been "rechambered" to 38 special or your gun has an oversized special chamber neither of which is good for 38 special case life.
Not dangerous to fire 38 S&W round in 38 Special chamber if gun will chamber them.
Gary