For the purposes of the specification, it looks like 'intensity' is the power per unit area received at earth. The apparent magnitude has a log-scale definition using the 'intensity', and in common language, this scale tells you how bright a star looks from Earth.
I think the specification classes 'brightness' as characteristic of the star i.e. a star that outputs more energy is brighter. This is related to the absolute magnitude of the star because the absolute magnitude is the apparent magnitude it would have if it were at a distance of 10pc.
Thus, the absolute magnitude brings all stars to 10pc and then gives them a magnitude at that distance. Stars with larger brightness will, therefore, have more absolute magnitude.