2 separate cartridges. The .38 S&W uses a .360 bullet where the .38 Spl uses a .357 bullet. The .38 S&W case is a tad larger (fatter). It was common to take S&W M&Ps which were chambered in .38 S&W and ream the cylinder so the longer .38 Spl would fit. Not good results. Because the .38 S&W cartridge was a larger .38 Spl rds would often split cases. Since the bores in the .38 S&W was for a .360 bullet accuracy with the .38 Spl wasn't the best either.
These were in the K frame guns. The .38 Spl operates at higher pressure than .38 S&W.
You say your gun is a .38 S&W hammerless. Top break? These smaller guns are not going to handle the higher pressures of the .38 Spl. The cylinder may not be long enough either.
If you want a .38 Spl for birdshot then get a .38 Spl gun. However, birdshot usually doesn't work all that well on snakes unless you're really close. Like 'stepped on them' close. If you're that close already you're better off with a solid projectile instead of birdshot. Birdshot in a .38 doesn't turn it into a shotgun.
This is a picture of both a .38 Spl and a .38 S&W.
