brightness has a specific meaning in IM as it relates to the colorspace HSB which is a hexcone colorspace, where brightness = max(r,g,b). intensity is the same as -colorspace gray. you can see all these by comparing formulae from the page for fx
http://www.imagemagick.org/script/fx.php where it says:
intensity: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue
lightness: pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)
luminance: pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue
to those listed on the page for colorspace at
http://www.imagemagick.org/script/comma ... colorspace
Gray = 0.29900*R+0.58700*G+0.11400*B
HSB brightness=max(R,G,B);
Rec601Luma Gray = 0.29900*R+0.58700*G+0.11400*B
Rec709Luma Gray=0.21260*R+0.71520*G+0.07220*B
YCC, YIQ, YUV Y=(0.29900*R+0.58700*G+0.11400*B)
Thus Gray (from -colorspace Gray), Intensity, Rec601Luma and Y from YCC, YIQ, YUV are all the same. Similarly luminance and Rec709Luma are the same.
Lightness=(max(r,g,b)+min(r,g,b))/2 (average of highest and lowest values channel values)
Brightness=max(r,g,b) (just the highest channel value)
You can get the mean for any, either directly or by separating out the appropriate channel first, as in my examples in my last post, depending upon which one you want.