The .357 round is a smidge longer and contains more powder, therefore, more velocity which results in more recoil (kick).
I bought a Ruger sp101 38/357 revolver. I read reviews on it prior to picking it up, and watched videos of its use. I have not been disappointed. It's ludicrously easy to load, fire, and clean. Aiming was easy, and the kick wasn't nearly as bad as I was led to believe - with the .38 rounds. I haven't fired the .357 rounds yet, which I'm told yield a harder kick. Since a .38 is thicker than a .357, I'm wondering why that is.
Grains are a unit of measurement (weight) The heavier the bullets "grain", well, the heavier the bullet naturally. Grains of powder refer to how much powder is in the casing. Essentially, the .357 has a longer casing and more powder.
I thought it was the grain count, but I thought the grain count referred to how many grains of gunpowder where in the bullets. A rep at the gun store told me it's a measure of weight. If someone could give a very basic explanation of why the .357 is more powerful, I'd appreciate it.