"Because it's not exactly the same as hue in HSV, it's named c (for chroma)."
As best as I can tell, this is actually misuse of the word "chroma"; usually it's used to denote something close to saturation of a color. Here are some references:
CSL is effectively a variation on the Munsell color system, which uses as its dimensions hue (your "chroma"), value (your "lightness"), and chroma (your "saturation").
I recommend changing the name/dimensions of CSL to HVC (or HLC, HCV, or HCL), to conform to existing use of that term; it's not too ambiguous since traditional HVC is referred to as "Munsell" and uses completely different units.
Parenthetically, using "saturation" in this context is a bit off, as well. Saturation usually indicates the degree between pure grey and the peak colorfulness of a color; whereas chroma is a measure of human perception. Fully-saturated blue has a much higher chroma than fully-saturated cyan. You can see this in your CSL toy, where the "S" (chroma) of cyan has a much smaller range than the "S" of blue.
Which is why I recommend still including the word "chroma" in the name of the color space, but to represent a different dimension.
"Lightness" and "value" are about as correct as each other. I recommend "value" to conform to Munsell, but "lightness" to conform to CIE Lab* makes as much sense.
The reason I bring this up is because I was playing with your excellent color toys, and I kept being confused by the definition of "chroma" which differed from the traditional one.
Thank you so much for making these things, regardless of whether you indulge my silly little request! I'm learning color theory/science/math, and playing with your sliders is a huge help.
Ha, in fact, I was pretty sure that I didn't invent something new. I will change the name as you suggested. Many thanks for dropping by!