Loads make an incredible difference. I shot some factory loads, 125 gn. IIRC, in my 686 2-1/2" bbl and after the first round, I knew I would empty the cylinder and that would be that. The recoil was incredible, and I'm not recoil sensitive, but I do recognize pain when I feel it.
I later shot some different .357 mag SD factory loads in my model 66, and the difference was absolutely amazing - even in the lighter, smaller gun, the recoil was nothing like the other loads.
As for why buy a .357 mag and shoot .38 spcl., one reason is because it gives one the option.
And, BTW, if there's no difference in recoil between a .38 spcl and a .357 mag, then there's no difference in energy - think about it. The same gun, two different rounds same bullet weight, produce no significant difference in recoil, how can that be? Only one answer - no significant difference in power.
There's no magic here, you accelerate a 125 gn bullet out of a given gun at a given rate of acceleration, it doesn't matter if it's a .357 round or .38 spcl round, everything is the same. Conversely, if a .357 has significantly more power, i.e. velocity for a given bullet weight, then it has a proportional greater amount of recoil.