I could get a little intuition about preset, poset, and toset. e.g. A toset is, in effect, a linearly ordered set, and a poset is a set in which no more than one element in the same order exists, although not all elements need to be comparable.
But I thought, if I knew where this definition was initially needed and how it appeared, I could get a better understanding. And it was hard for me to find out enough explanation. I'd appreciate it if you could let me know about this. In addition, if you have any references to the history of other ordered sets, please recommend it.