High Brass and Low Brass are just marketing tradition these days. However, in the era of hulls with paper basewads there was indeed another reason that had more to do with the internal basewad height.
story behind the brass went something like this:
Heavy loads required more internal room in the hull that was provided by a low internal basewad. Paper basewads were not perfectly gas-tight and a low basewad needed the reinforcement of a high brass head to maintain hull integrity. Lighter loads that did not need the internal room used cheaper to make, high paper base wads and low brass case heads. Thus high-brass shells had a low base wad and were used for heavy loads. Low brass cases had a high internal base wad and were used with lighter loads.
Into the 1960's it was not uncommon to refer to low base hulls and high base hulls - meaning high brass and low brass respectively. Got it?
Today high brass is simply traditional marketing for heavy loads. However, many low-recoil buckshot loads are put up in high brass cases.
Shotshell handloaders can, of course, shake-up non-handloader assumptions with visually disparate creations like this: