I break down tents, tarptents and tarps in the following manner.
Tents - When you purchase a tent, your getting a complete and fully functional shelter. It'll contain everything needed for proper setup. Including tent body (sometimes single wall and sometimes double wall), poles and stakes.
In general a tent requires the least knowedge on the part of the user to get a fully functional shelter.
Tarptents - With a tarptent, you're looking at a shelter that attempts to combine the best aspects of both tarps and tents. Like a tarp, they tend to be more open with lots of ventilation. Since they are single wall, this is a necessary trait to minimize condensation. Unlike tarps they will have some form of netting to keep flying insects at bay. And these days most tarptents have some form of floor.
Structure wise, tarptents maybe setup in multiple ways. These include, using your hiking poles, optional poles or even hung from a tree. In any case which structure you decide to use is left to the user.
Also, tarptents tend to be more picky in terms of site location. This requires additional knowledge on the part of the user to maximize the benifit this shelter has to offer.
Tarps - Traditional tarps were flat and rectangular. Today they show up in all shapes and sizes. As with tarptents, tarp setup is left to the user to decide. Since tarps lack floors, site location is critical. Without netting, using tarps in bug season can be problematic.
Historically what we call a shaped tarp today was called a tent. For hundreds of years tents didn't have floors or even netting. Our idea of a tent, a double wall shelter with floor and structure, is only about 60 years old.
shaped Tarp / NetTent Combo - Here's where we try to push the tarp back into the tent world, but not all the way. Again many people like the protection of double walls. They can be warmer and the inner wall helps keep you away from the condensation soaked canopy.
However, unlike tents, they don't have a defined structure. Again it's up to the user to decide how to best setup the shelter to meet their needs. In addition the outer and inner shelters are designed to be used independently.
While it true that some tents can be used in so called "Fast Pack" mode, many if not most can't. And even if your tent components can be setup independently, you're still stuck using the defined pole setup. I know of no "Fast Pack" mode tents that allow you to also leave your poles behind and use your hiking poles.
In today's world of shelters there's obviously significantly more choices. However, making the right choice frequently requires more involvement and understanding on the part of the purchaser. For new campers, making the best choice from the myriad of options can be a daunting challenge.
"So maybe the difference is that tents need dedicated poles, and tarps do not? But that's a pretty fine difference, since the bigger concern is about function." Andrew.
The difference between a fine line and major gulf is frequently a matter of knowledge. What appears to be inconsequential to an experience hiker maybe overwhelming to someone new to the game.