One source of the confusion is that some of us refer to all lightweight single-wall tents using "tarptent" as a generic term. This practice is grossly unfair to a really nice guy named Henry Shires, owner of Tarptent.com, and is also a violation of intellectual property (copyright/patent) laws. I've stopped doing it (or have at least tried to!). "Lightweight single-wall shelters," although more cumbersome, is more descriptive. It's also fairer both to Henry and to the other makers of such shelters as Six Moon Designs, Gossamer Gear, Anti-Gravity Gear, Oware, Mountain Laurel Designs, Titanium Goat and others I have probably (and inadvertently) omitted.
The original Tarptent that Henry Shires invented (for his own PCT through-hike) was intended to combine the best features of a tarp (lightweight, airy and plenty of ventilation) and a tent (bug-proof and all in one piece, so less complicated to set up). Originally they had no floors. Later a sewn-in floor was added as an option. By now, you have to special order to get a shelter from Tarptent without a floor! Since a floorless shelter requires a separate ground sheet, the actual weight saving of omitting the floor is minimal or nonexistent. Some other manufacturers still sell floorless shelters, especially pyramids that may be used for snow camping.
Lightweight single-wall shelters may or may not require one or two trekking poles for support, although most do. The reason to use trekking poles is to save weight by supporting the shelter with a dual-use item. For non-trekking pole users, regular tent poles are available from the tent manufacturer although this destroys part of the weight savings. This weight savings is actually semantic--since the primary use of trekking poles is to support and balance the hiker, not the tent, they aren't counted in tent weight. If you use tent poles and don't take trekking poles, then the tent poles are lighter than most trekking poles! Also, most folk use trekking poles to support their tarps. When the tarp added sewn-in bug netting and morphed into a tent, the custom of using trekking poles continued. A few lightweight single-wall shelters come with their own poles and don't need trekking poles for support.
I hope this description helps clarify the situation!