Is there gray light?
No, just a dim white light.
No, just a bright black light.
What is black light?
…a purple light, that some say is black.
OK seriously, the term “gray” only makes sense for the color of an object, not the light itself. Gray means it reflects a small but equal fraction of all colors. But if you have a 100-watt bulb and define it as white light, I suppose you could call the output of a 5-watt bulb as being gray. It depends on the context.
No not that type. 
Black is all visible frequencies being absorbed, reflecting or transmiting none.
Grey is all visible frquencies being absorbed to the same extent but not completely, reflecting or transmitting all visible frequencies to the same extent.
Remember, a blackbody radiator, such as a filament will shift from cooler red to hotter white as the temperature increases.
Grey is not a colour. Pure colours (hues) can be added to white, black or grey to form tonal colour families.
If you want, you could think of white being complete illumination, black being total lack of illumination and grey being the degrees inbetween.
I can challenge that notion with a few photographic examples. One common tool is an 18% gray card used as a light metering standard. In “normal” illumination it looks gray but the intensity of the light can be altered so it looks near black or pure white to the viewer. Sometimes black background cloth or paper is used to achieve a white hotspot with a studio flash or color by adding a gel.
Our perception of light and dark and even the color of “white” is an ambiguous one as our eyes are constantly adjusting to conditions. In some ways we are far more flexible than any camera which makes it harder to duplicate how we piercieve what our eyes see.
Radiation from a body that has uniform emmissivity at all wavelengths, but the emmissivity is less than one, is called “graybody radiation”. (If the emmissivity is 1, it’s called “blackbody radiation”.) So “gray” light can be construed as light that has the same relative spectral emission as blackbody radiation, but lower intensity than would be expected from a blackbody at the same temperature.