The different displays show whether it is a "driven" or "driving" dimension.
if you click on the black dimension it lets you change the number, if you click on the grey dimension it brings up the dimension options in the command manager
black dimensions are driving (you can change) - grey are driven (defined in another file)
To add to what has already been said, the grey dimensions are typically reference dimensions meaning that either that exact dimension
is duplicated somewhere else of the dimensioning scheme is such that grey dimension is over dimensioning.
What I used to do as a CAD Admin is set the color of the driven dimensions to a dark grey, so you can still tell the different on your monitor, but it didn't show up noticably different when printing. The color can be changed in Tools>Options>System>Colors>Color Scheme settings. The setting is Dimensions, Non Imported (Driven).