Looking at posts and reviews on a lot of sites, it is clear that lots of people use a S&W 357 SIG barrel in an M&P 40, and get excellent results. Any time you fit a major component like a barrel, you should not be surprised if you need to do some fitting, but the S&W factory replacement barrels seem to be properly toleranced to work nearly every time without fitting.
Storm Lake barrels are "match grade." Any match grade component is going to be tighter-fitting than factory replacement parts. This is to allow hand fitting for a precise fit. Since modern manufacturing methods allow much closer tolerances than just a few decades ago, match grade components will more often function without modifications, but you can't count on it.
When a properly fitted match grade barrel is installed, you can expect a noticeable improvement in accuracy, but should also be aware that you can get less functional tolerance to dirt, temperature and other adverse conditions.
As for magazines, both magazines that came with my S&W 40c have both "40 S&W" and ".357" stamped on them, even though S&W does not presently make a 357 SIG pistol that this magazine would fit.
