.38 S&W Reloads
It's doable, but the .380 bullet is a little undersized (.355"), so don't expect great accuracy. Also, it might not grip the sidewalls of the casing very tightly, and bullets might move forward under recoil. If you try it, I'd stick to .380-level loading data and watch for bullets backing out of the case.
My favorite (and only) .38 S&W load uses 125 grain lead bullets (sized .358) and 3.5 grains of Unique. Information on the .38 S&W says the bore is .360", but I find that .357-.358" bullets work fine, with good accuracy in my two breaktops, one of which is a S&W 4th model DA with a 6" barrel. I don't particularly like shooting it as the grip is uncomfortably small for my hands.
.38 S&W factory loads are always OK in your revolver, as they are loaded on the light side because so many of the old breaktop revolvers made by many different makers are still out there. Manufacturers don't like liability lawsuits resulting from someone's old junker revolver blowing up in his face while firing their ammo. Later model S&W or Colt revolvers with a swing-out cylinder chambering the .38 S&W can safely use a little hotter loadings giving performance approaching that of the .38 Special. In fact, a lot of the WWII S&W Victory models chambered for the .38 S&W (.38/200) for the British military had their chambers bored out to accept the longer .38 Special cartridge after the war for sale on the US civilian market. Not a good thing to do for several excellent reasons, but it worked. That's what L. H. Oswald allegedly used to shoot Dallas police officer J. D. Tippett. By the way, that's a very interesting ballistics story, but I won't go into it here.