Take a look at these cartridges side by side:
They are not the same. If you have a gun that can fire both, you'll feel the difference when shooting. But this isn't really the question; rather, the issue is what to load your .38 revolver with. There's a lot of opinion about that. High-performance ammo like CorBon DPX JHP will get the most out of your .38 caliber revolver. I use it in my S&W 638, because in any ranking of SD ammo, it consistently performs at or near the top of any comparison, and the expansion is second to none.
I also have this:
Both wad-cutter and semi-wad-cutter lead-nose ammo have an excellent reputation for getting the most out of the .38 spl round. As a matter of practicality, you'll find that a .357 revolver is a lot of weight to port around. Very doable, sure, and a lot of people opt to do that, but personally I've found the .38 airweight revolvers from S&W to be far easier to carry. They're in the "forget you're even carrying" category. Load with solid SD ammo and you're good to go.