As for invisible floor, I would agree that the clause "This is to draw the character without drawing a background" literally describes simple background and is causing some confusion. invisible floor should be able to exist independent from if the background is drawn or not.
invisible floor implies that characters are interacting with what would be a floor, but is, of course, not visible. It seems to be a tag similar to *_on_glass from_below, but without the visual indicator of glass (the streaks).
I think a lot of the confusion stems from characters no longer interacting with a visible, physical environment (i.e. standing on nothing, sitting on nothing, existing in a nothing space). The *_on glass tags somewhat helps, but when there is truly nothing there is something I think I have yet to understand.
I think invisible floor should be able to exist with simple background, as they are two independent ideas (albeit the wiki for invisible floor couples the two together, that should be changed).
Another problem with this tag, too, is that when it's used with simple background, well, the floor isn't invisible. The floor is right there in solid color; the shadow casted by the character also implies that the floor is solid and is VISIBLE. An infinity cove describes the space of the invisible_floor simple_background, especially when the floor is present. post #4930744 and post #9965876 as mentioned by OP truly describes the invisible floor.
I think a rewrite of that wiki needs to be done before this BUR goes. And even then, I still think these two tags are independent.