TI pretty clearly distinguishes between LDOs and other categories of linear regulators on the basis of using a FET pass element (which is true of neither the LM317 or the LM7800 series, both are Darlington-based).
It's not really clear from this paper, it is more handwavy based on today's circuits.
They claim that the darlington voltage drop is ~2V which is suitable for 5V to 2.5V regulation, and then introduce 100mV with an NFET as low-dropout for cases where LiPO cells are 3.6 V, or 300 mV above industry standard 3.3V (or the new embedded expectation of 1.8V or 1.2V off a 2x 700mV cells).
However, what if I need to regulate 3.35 V to 3.3 V, do I need an Even-lower LDO (ELLDO)? That meants we have HDO (2V), LDO (.1V), ELLDO (0.05V), which becomes an absurdly semantic situation.
I think the confusion is that engineers picked the words and it is based on the technology of a current point in time. In their mind, the breakpoint is NFET dropout of 100mV, which is purely subjective. Although I could also argue that my example is silly because it is within the range of tolerance of most datasheets spec for Vin of 3.3V +/- 1%.
I'll agree that it's largely a semantic difference and that I overstated the significance of the MOSFET involvement as the pass element - you can design single-transistor PNP elements with only a few hundred millivolts dropout, and at one point TI referred to these as LDOs.[0] Indeed, even the Sziklai pair gets called "quasi-LDO". Individual engineers likely have different personal thresholds for what constitutes an LDO. But it's worth pointing out that in practice there are only a handful of plausible linear regulator pass elements, and the physics of the BJT-based pass elements sort them into a distinctly higher minimum dropout voltage than what is achievable with MOSFETs.
I still stand by the characterization of LM317 and LM7800 family as "not LDOs". Both devices are Darlingtons with at least two Vbe drops across the series pass element. On the continuum of LDO------Not_LDO, both LM317 and LM7800 are firmly on the Not_LDO side.
See section 2: https://www.ti.com/lit/ml/slup239a/slup239a.pdf