Other than tradition, there is no legitimate reason I can think of, why the .38 Special is loaded with a heavier bullet than the .357 Magnum. When the .38 Special was introduced....if memory serves, this was around 1902.... it was originally loaded with a 158 grain, roundnose bullet. I believe its origins go right back to the blackpowder era, percussion .36 caliber Navy Colt. In any case, that bullet became the standard for the cartridge and remains so, today. Most folks consider the 158 grain bullet....including myself...as a versatile, all-around performer for use in the .38 Special cartridge. Including target shooting. That being said, I started shooting the much lighter, 125 grain bullet in this caliber some years ago, as it offered about the same level of accuracy, with far less recoil and muzzle flip. An advantage in competitive shooting.
The .357 Magnum....I believe introduced around the mid-1930's (Don't have a reference in front of me, so again going by memory) began life as a self-defence round, and continues as such today. A 125 grain, high velocity jacketed bullet turns this relatively small caliber round into a formidable man stopper. This is one of the reasons why many police departments adopted it when it was first introduced. So, the most commonly found loading for this round today, is still a 125 grain, jacketed bullet. Personally, I believe the 158 grain bullet is a better performer in the .357 Magnum...especially where used as a short range hunting round. Plus a general purpose target round. But, the 125 grain bullet does perform quite well, when matched with a suitable powder. I also adopted the 125 grain LRNFP bullet for use in my .357's, as it offered the same advantages in competition, as its .38 Special counterpart: Speed.
Hope this makes sense.