Regarding entropy and the 2nd law of thermodynamics, what is the relation between equilibrium and disorder?

I'm confused between a) maximum entropy of a closed system = disorder; b) max entropy of a closed system = equilibrium (or statistical probability distribution that elements in the system will be in such and such a predictable state. [one ex of b is the 'pixel hopper' [at http://en.wikibooks.org/wiki/Entropy_for_beginners]]. Why is equilibrium a disorder, necessarily? [No problem if I think of an ancient ruined city which is now a jumble of stones that used to be organized into temples, but if they disintegrate in patterns?] So why can't organized things be in equilibrium? like a diamond (either now and 50,000 years from now)? Maybe given enough time that too will break down, at which time its supply of potential energy will have dissipated. Is the difference between the relative equilibrium of non-entropic systems the fact that it could be (or could have been) all sorts of things? But the equilibrium of entropy is just one (predictable) state?