"Crossover" was essentially "minivan without sliding doors."

4x4 generally means "you have a second gear selector to choose 2wd or 4wd Hi or 4wd Lo," whether that selector is a mechanical lever or a switch.

"Full time 4wd" and AWD mean that the car is always driving all four wheels, there is no selector to switch to 2wd, and usually with the primary being front wheel drive, with a teeny driveshaft sending a small percentage of the power (like 20% or 30%) to the rear wheels (though that may change based on traction control sensor inputs).

I apologize for the length of the previous sentence.

Every definitive trait has some counter example that still counts because people “feel” it’s good enough.

There's an aphorism in statstics / science: "all models are wrong, but some are useful." I feel that the distinction between genuine off-road-capable SUVs and crossovers/tall cars/glorified station wagons or minivans is useful, even if it isn't completely definitive. Generally speaking, if it's a unibody vehicle it probably isn't very good off-road, and therefore doesn't really deserve to be called an "SUV."

So does a 2wd “suv” (by your definition) then get declassified?

A 2WD SUV is less general-purpose, but I think they still have enough potential to count (think desert-racing prerunners, which are often 2WD but legitimate off-road vehicles).

Plenty of large "tall station wagons" are unibody. About the only legitimately capable offroad 4x4s I know of that are unibody are the Jeep Cherokee (the old one) ~~and maybe something like a Suzuki Jimny~~ (edit: nope, even that tiny thing is body-on-frame).

(Consider the difference between a (unibody) Toyota Highlander and a (body-on-frame) Toyota 4Runner, for example: only the latter is a "real" SUV, in terms of being capable off-road.)