I can answer that definitively for PADI, since I wrote the new language on this which they will publish in the future. They previewed it in the professional journal two years ago.When referring to overhead environment, I've done a couple wreck dives and the last thing I would consider myself is a tech diver. It wasn't a complicated wreck but I penetrated and went through 3 levels in a vertical exhaust stack. I know there's a difference between a cavern and cave (certain# of feet to accessing vertical ascent?). Does the same distinction apply when classifying a wreck a technical dive?
Start by differentiating between a swim-through and a penetration. In a swim-through, you enter at one point and exit at another. In a penetration, you exit at the same point where you entered. In each case, especially swim-throughs, the range of difficulty and risk begins with such an easy situation that even the most beginning of divers can do it safely. In fact, simple swim throughs can be done on OW training dives.
A simple swim through might be only a few feet long, with bright sunlight and no complications. They can then be more complicated, with greater length, darkness, obstacles, silt, etc. The presence of these complications creates greater risk, and greater risk calls for greater training, skill, and/or equipment. It is up to the diver to determine the level of risk the swim-through presents and use good judgment about his or her ability to manage it. In general, the same kind of criteria that differentiate between a cavern and a cave apply to the line between recreational and technical.
The same sort of progression applies to penetrations. Many penetrations are only a few feet into brightly lit areas. Anyone can do them. Eventually you reach the point of laying line to guarantee that you can find the opening again, and if you do that, you should have good training for that. In general, the same kind of criteria that differentiate between a cavern and a cave apply to the line between recreational and technical.
The old PADI wreck course (which is very poorly done) does not even mention swim-throughs. They are considered open water. The failure to mention them fools people into thinking that their descriptions of penetrations refers to every possible entry, and that is not true. You don't need to lay line to swim through the wheel house.
I go to South Florida every winter, and the area around Pompano Beach is littered with shallow wrecks that can be entered without any technical training.