What is the difference between 375 sign bullets and 9x19. Bullets?

Bullets themselves are basically the same between 9mm and 357 Sig. But it's like 40S&W vs. 10mm Auto. One has a lot more power behind it. 9mm and 40S&W are good, but 357Sig and 10mm are more powerful.

So reloaded I can use the 115 and 124 great 9 mm  bullets I have in stock to load it?

It seems there are some bullets designed specifically for the .357 Sig. I believe they are a little shorter with a more blunt profile compared to your typical 9mm bullets. Has to do with short case neck, cartridge OAL, and still being able to fit in the magazine.

I wouldn't buy a pile of bullets until you can confirm they will work with your gun/magazine.

That said, since you posted this in the Machinegun section, what are chambering this cartridge in?

I have a .357 Sig barrel for my Uzi, and it won't feed for anything. 9mm, .40, and .45 all run great in the same gun.

Bullet setback is also an issue so you want to run powders that fill the case. It's more like loading a bottleneck rifle cartridge than a pistol cartridge.  Depending on barrel length you can also hit velocities above what are recommended for plated bullets.

If speed is your thing, you might try the 9mm 80 grain all copper Barnes TAC-XP hollow points in your .357 Sig.

I might add that I have and MP5 in .357 Sig and the weapon shoots full auto with a registered sear just fine.