If by "light brown" you mean like a tan or khaki color, it would have to do with saturation--that is, sort of "watering down" the color with some blue tones. Neutral colors like gray and brown typically have a mix of a wide variety of colors, gray being the "true" neutral and brown being a bit heavier on the red/yellow tones.
Is saturation representing the share of pure color (i.e. only reflecting a certain wavelength), and brightness representing the intensity of color light coming/reflecting to the eye?
In other words, brown differs from orange in brightness (i.e. the amount of light reflected), and light brown differs from dark brown by saturation (i.e. the share of that paint vs., say, white)?
So it's actually light/dark orange, but the paint is made so that it only partially reflects orange, and we see it as brown?
But isn't it the same as adding black? And if we do add black to orange and then white, we do not come back to original orange (since now it's kinda orange+grey), but arrive at light brown?
Sorry for so many questions, trying to build intuitive understanding of the matter
"Brightness", in my experience, generally refers to the amount of light reflected (or sent from the light source). It doesn't directly affect the perceived hue, it's just a measure of how much light there is. It's hard to get an intuitive sense of brightness, because of how we perceive color.
Saturation refers to the "purity" of the color--that is, how much light it reflects of other wavelengths. Gray reflects visible light in equal proportions, which makes it the least saturated. A surface that reflects only a single wavelength would be considered fully saturated, and appear as a vibrant hue.
It might be more helpful to think about how our eyes receive different wavelengths. There are three colors we perceive: red, green, and blue. The closer the reflected wavelength is to these colors, the more those "sensors" in our eyes are activated. So for example, yellow activates the red and green sensors about the same amount (and less than pure red or pure green), so we perceive yellow. Orange is mostly the red sensors, with a little bit of green activated as well.
We perceive brown when the blue sensor is also activated by some amount, because brown reflects a little bit of blue light (as opposed to "pure" orange, which wouldn't have any blue light reflected). The lightness/darkness of the color is mostly the overall amount of light reflected (the brightness), but the big difference in what we perceive is that little extra blue light that brown reflects, that orange doesn't.
Brown is still considered "dark orange" because the primary wavelength that it reflects is an orange color. And dark browns don't need to reflect any blue light to be considered brown. But lighter brown shades will reflect a greater proportion of blue light than "light orange" would at the same brightness.
To get some intuition around saturation and lightness, try out a color wheel. Start with a color like #A68768 and then play around with the saturation level (labeled "S" in "HSL"). Have fun!