I recently learned 青色をしている as a synonym for 青い, but I don't have a good idea of what the difference is, or even if there's any difference at all.
On chat, Flaw suggested the difference might be intrinsic quality (〜をしている) versus incidental quality (青い), but I don't have a good idea of what that means. I found a forum thread suggesting something similar, but I came away from that a bit confused--one poster claimed it was intrinsic versus extrinsic but didn't explain what that meant, and another said there is no difference in most cases.
So my question is: what is the difference between 青い and 青色をしている?