Is the cartridge of a caliber .357 can load and fire on caliber .38 revolver?

No. The .38 Special cartridge can be fired in a .357 Magnum revolver - and only a revolver, which does not require chamber headspacing - but it doesn't work the other way around. The .357 Magnum cartridge is too long to fit into a .38 Special cylinder, and the .357 Sig cartridge is in no way compatible, either with the .357 Magnum or the .38 Special.