HunterLab is similar to Cie-L*ab. Both are based on Xyz but HunterLab's color coordinates are based around a square root transformation rather than a cube.
Cie-L*ab is defined by lightness and the color-opponent dimensions a and b, which are based on the compressed Xyz color space coordinates. Lab is particularly notable for it's use in delta-e calculations. Read more about it here.
Color conversions performed using the open source ColorMine library.