The two cartridges have nothing in common other than the number in the name and velocities with like bullets. You may or may not be able to easily find .357 Sig ammo and brass or a pistol chambered in it.
The .357 Sig is a rimless, bottle necked, cartridge that uses .355" bullets. Velocities are in the 1300 to 1400fps range with a 125 grain bullet.
The .357 Mag is a rimmed, straight walled, cartridge that is 1/10" longer than a .38 Special. Its bullet measures .357" and can weight up to 168 grains.