After the exposure blending function called HDR in Lightroom was added I have entirely used that for situations where I needed more DR than my camera could provide. The HDR name is in fact in my opinion misleading since the word HDR is such a loaded one.
It's mostly caused by a loose use of terminology.
There is 'HDRI' on the one hand, and there is 'tonemapping' on the other hand.
HDRI, the imaging part, has to do with capture processes that allow capturing a large range of luminance levels, either by using low noise + high saturation level sensors, or by the adding of multiple levels of exposure (e.g. by EV bracketing) which allows exceeding the range possible from a single capture.
The tonemapping part is basically something we already used, e.g. by applying an S-curve Levels adjustment, but for images with huge dynamic ranges that would still result in relatively low local contrast. That's why locally adaptive luminance adjustments do a better job, let's call it 'HDR tonemapping'.