Another look at the units:
PAR (Photosynthetically Active Radiation) - Those wavelengths between 400 & 700 nm. There is no information on the actual spectrum or the amount of light being projected.
PPF (Photosynthetic Photon Flux) - How much light (number of photons) is leaving the source per unit time. It is a constant (ignoring lamp degradation).
PPFD (Photosynthetic Photon Flux Density) tells us the number of photons per unit time hitting a unit of area. Because photons spread out as they leave a light source, this is dependent on distance from the lamp, and is closest to lumens or lux, albeit plant-centric rather than human eye-centric.
(Theoretically, if all of the photons were collimated, with no losses to the sides, the PPFD would be independent of distance - think of a lamp made up of an assortment of lasers having PAR wavelengths, all pointing at your plant, or 100% of the output of a LED panel "piped" to your plants through optical waveguides.)
Thanks Ray! Yeah, this discussion has really helped clarify some things for me. I think this brief, basic, discussion of units and metrics is sorely lacking in many of the sources that try and explain PAR/PPFD online (even the most basic ones that try and explain things from the ground up).