I encountered HLS = Hue, Lightness, Saturation the first time here:
(1) J.Encarnacao, W.Strasser (diacritical characters simplified*): Computer Graphics, Oldenbourg 1986
(2) Foley, van Dam et al: Computer Graphics, Addison-Wesley 1990..1993
(1) contains an early reference to Wyszecki:
G.Wyszecki: Farbsysteme. Musterschmidt, Göttingen, 1960.
(1) and (2) mention Smith:
A.R.Smith: Color Gamut Transform Pairs, Computer Graphics., 12, 3, Aug.1978
It's safe to say, that L means Lightness. Luminance is a physically measurable quantity.
Lightness is used in HLS in the same sense as in CIELab.
Luminosity is a somewhat vague Photoshop nomenclature.
Using HSL instead of HLS is merely misspelling, quite common though.
[*diacritical characters: ordinary characters with tilde and accents etc.)
Best regards --Gernot Hoffmann