The Wikipedia article on Blend Modes describes three of them in particular like this:
Photoshop’s hue, saturation, color, and luminosity blend modes are based on a color space with dimensions that the article HSL and HSV calls hue, chroma, and luma. Note that this space is different from both HSL and HSV, and only the hue dimension is shared between the three; see that article for details.
Because these blend modes are based on a color space which is much closer than RGB to perceptually relevant dimensions, it can be used to correct the color of an image without altering perceived lightness, and to manipulate lightness contrast without changing the hue or chroma. The Luminosity mode is commonly used for image sharpening, because human vision is much more sensitive to fine-scale lightness contrast than color contrast. See Contrast (vision).
and, without references, adds:
Few editors other than Photoshop implement this same color space for their analogs of these blend modes. Instead, they typically base their blend modes on HSV (aka HSB) or HSL. Blend modes based on HSV are typically labeled hue, saturation, and brightness. Using HSL or HSV has the advantage that most operations become invertible (at least in theory), but the disadvantage that the dimensions of HSL and HSV are not as perceptually relevant as the dimensions of the space Photoshop uses.
In my version of Gimp, those options are Hue, Saturation, Color, and Value. This isn't exactly the same as the terminology used in Photoshop (value replaces luminosity), but it's also not "hue, saturation, and brightness" as in the paragraph above.
As the Wikipedia article explains it, the color space Photoshop uses here would appear to be an advantage for photography, since it's more perceptually-relevant. Which does Gimp use?