We're on a complex topic, lighting and it's measurement, that does not warrant one or two sentence responses. But I'm going to try and keep it as simple as possible for anyone who is new to this.
Any band pass type light meter is simply reading a net photon energy level.
A quantum meter is typically calibrated for sunlight and is not corrected for human vision sensitivity. It measures whatever net light energy is sensed and converts it to the calibrated numerical value between 400-700nm. It has no idea where it is landing in that range. I can actually take a PAR reading of a monochromatic green emission at a peak of 555nm and still read a high PAR value. A quantum meter does not utilize an algorithm that would avoid this region (if this is what Kite meant I take exception and if not forgive me as this is what I interpreted your statement to mean) and weight the PAR measurement more towards the red or blue bandwidths. A quantum meter will measure the blue spectrum's in higher PAR energy values than red spectrum's as the blue regions pack 1.5x the energy as the red regions. This relationship is defined in Planck's Constant as a quantum of action in quantum mechanics whereby, for example, a 400nm photon has 1.5X the energy of a 600nm photon. The quantum or PAR meter will read this value as such. It's just measuring the photon energy at the sensor.
A photopic light meter is corrected for human vision sensitivity (photopically corrected) and gives measurements in lux or footcandle readings and will have been calibrated to a certain kelvin value. These values are based on the human vision luminosity function whereby the highest photopic value is 555nm and the scotopic value is 505nm. This chart represents the peak photopic and scotopic values and the various points on the curve where human visual perception decreases.
If anything a value that does not exist today for plant lighting should be created that represents a something in a Par/Lumen value whereby the PAR/Lumen (I made this term up) value would take into account the weight of energy at a given point on the plant sensitivity curve. But since this value doesn't exist (akin to lumens but more in line with a composite lumen:CRI value) all you can do is look to the spectral distribution charts to see relative intensities that the lamp emits to determine if you're catching the wavelengths you're looking for. If you're going through all this and still considering purchasing lights or lamps from a manufacturer that refuses to publish their spectral distribution graphs because they claim their spectrum's are proprietary than I have a really good deal on a bridge for you. What these manufacturers are essentially telling you is to buy our product based on just our claims and not the essential data you should expect that is as a minimum necessary to make an informed decision of your own.
At the end of the day you still have to determine what these values represent to you as the end user. For example the lumen is quantity and the CRI is quality. Which is more important as the balance between these two is ultimately up to you to decide. In plant lighting striking this balance between energy and spectrum is of even of greater importance since it will spell the difference somewhere between crop success or failure.
Even when presented properly it's easy to get confused as this is a complex topic. If you take nothing else from all of this just remember; A PAR measurement will be better than a photopic value since these values are expressly meant to apply to human visual regions. But just a PAR value, as measured in how many uMole are striking the sensor at a given time, should not be used to determine if the light being emitted from a given light source has adequate broad spectrum blue - red to successfully take a garden to harvest. Therefore I use my quantum meter to determine if there is enough energy hitting the plants where I want the light and I use a historical reference from my previous grows to determine if the light being emitted is of proper bandwidth. This enables me to repeat grows successfully from veg through flower with a minimum amount of stress to either me or my garden. Lights/Lamps that regularly accomplish this and are energy efficient, stable spectrum, low heat and long life are likely going to find a spot in my garden.