My impression of "color force" is just that it's a convenient mathematical way of describing how the charges interact with each other. The idea (I think) is that color force exists only between two different color charges. One of the unique properties of the color force is that it decreases as the distance between two hypothetical "quarks" decreases, in an almost linear form. What this means is that it is impossible to separate the quarks (because eventually, you'd just create enough energy to suck up a new quark from the vacuum and create a new particle). This is consistent with the color model of the quark, because the net color of, say "green" and "anti-green" is white (another aspect of color charge is that the net color of a particle must be "white"; red green and blue add together to give white).