Is that difference spelled out somewhere in the PHB or DMG?
I'm pretty sure that the DMG says something about the difference between hard and soft - it's probably in the section called "The Adventure", and would relate to how hard it is to be heard when trying to walk quietly (I can't remember the precise mechanic - maybe the thief gets a bonus to hear noise against those wearing hard rather than soft boots?).
In theory, I can understand the difference between hard and soft. Hard (presumably) offers more protection, soft (again, presumably) offers more stealth.
But high and low?