Officially PAR is the 400-700nm range. Lux is supposed to be total radiation at a distance of one meter. Usually though it's calculated based on measuring some specific wavelength around 550-570nm since that's where the human eye is most sensitive, and assuming that the other wavelengths are putting out progressively more or less power.
Unfortunately modern light bulbs don't play by the rules. They put out varying amounts of light at defined wavelengths. Then of course when the spectrum shifts, it's hard if not impossible to tell by looking at it without some direct comparison. You can either use a lux or quantum sensor to compare a reading, or you can compare to a brand new bulb if your eyes are good enough.
Basically all of the light scales are work arounds to avoid having to copy down a spectrum graph. The same way decibels are used to describe volume without telling you pitch.
Basically they are trying to find a simple way to compare these with one number: