Yes, the same dies can be used for .357 Max, .357 Magnum and .38 Special.
But I recommend you get a set for .357 Mag and a set for .38 Special. That way, you can set the dies up for each cartridge and not have to mess with it every time you change from loading one to the other.
Since you have a 550, just set up a tool head for .357 Magnum and another for .38 Special. You'll never regret it.
As it is, if you load both .357 Mag and .38 Special if you are not diligent in your case sorting you'll either way over bell a .357 case in a .38 special adjusted die, or you'll have very little bullet seated in a .38 case coming out of your .357 adjusted seating die.
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You can shoot .38 Special in a .357 Magnum - no problem at all, just clean it on a regular basis to avoid a carbon ring in the chamber.
.357 Brass costs significantly more than .38 Special. You could shorten .357 brass to use in a .38 but it's a lot of work when .38 brass is plentiful and less expensive.
You can load .38 +P+ or .38-44 level loads in to .38 Special brass to use in a .357 Magnum revolver, or a .357 Magnum model revolver that was ordered in .38 Special (some police departments did that to avoid using ".357 Magnum" for PR purposes while still wanting .357 Magnum performance in a .38 case. However, that requires you to carefully separate those loads so that you don't blow up a .38 Special. revolver.
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Powders for .357 Magnum include:
- Unique (An excellent powder for short barrel, and or lighter recoil, but data is a little harder to find. It's also excellent for cast bullet loads.)
- H110/Win 296 (A good powder for maximum loads in longer barrels, but the heavier charges equate to a lot more recoil.)
- Alliant 2400 (Another good choice for near maximum jacketed bullet loads)
- Tite Group (A good powder for cast .357 Magnum loads.)
.38 Special:
Win 231, Bullseye, Unique, 700x and Power Pistol are all good powders for both cast bullet and jacketed bullet .38 Special loads. HS-6 works great for jacketed loads.
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The only real difference with .38 and .357 loading is that the .38 is an old case with a lot of capacity and the .357 Mag case it even longer. They both have a lot of extra capacity and both cases will potentially hold a double charge of faster burning powders. So get a light for your 550 to ensure you can easily do a visual inspection of powder level before you seat a bullet on it. And, anytime your routine is broken, stop and verify the status of every case on the shell plate before you pull the handle again. That's a given with any progressive press, but it's even more important with large capacity revolver cases like the .38 and .357.