To answer the original Poster's question about the ammo....
.40 S&W vs. .357 SIG
Both Casings are the same outer diameter dimension as well as effective overall length. Beyond that, they are different.
The .357 SIG necks down to hold a 9mm bullet (.355") and the casing itself is slightly thicker in the head end (it is not a modified .40 S&W, but a new design that is actually stronger than the .40 S&W)
Also, nothing else sounds the same as a .357 SIG firing. I don't care what gun you are shooting from, it has a totally different report than anything else I've heard.
Drop-in barrels generally work just fine as do the .40 S&W magazines for both rounds. Some manufacturers develop a unique .357 SIG magazine which will not feed .40 S&W, but this is limited to SIGARMS from what I've seen. Since the head and rim of the two rounds are virtually identical in their external dimensions, the action of the gun works just fine.
While I've seen .40 S&W mags feed 9mm jut fine into a conversion barrel, I HIGHLY recommend you take extreme care in following this practice. You do NOT want to ever chamber a 9mm into a .40 S&W or .357 SIG barrel. The result could be disastrous. .357 SIG into a .40 Barrel is also not a good idea, but at least it isn't likely to blow up on you.