You've basically got it, outside of a few misconceptions. Let me try to clear this up:
If you are moving inside of or stationary in solid cover, you get a Solid Cover bonus. Think of it like moving down a stone wall or standing at one; it'll cover you as long as you are against it.
For In Cover, you can only attempt it if you are standing still. When I game with unfamiliar players, I call it "Taking Cover" or "Going Prone". Essentially it's your guys making best use of the cover around them, and they can't be moving to do that.
For Being Exposed, it doesn't need to be solid cover or not. It could be bushes, scrub, any terrain piece which could provide concealment; it might not block a bullet, but you can make yourself harder to hit. So while bushes might not give you a Solid Cover Bonus, they prevent you from being exposed to the enemy.
So to give you a full cheat sheet list:Regular ForcesIn Solid Cover
Stationary: +1D for Solid Cover, +1D for In Cover Bonus
Moving: +1D for Solid CoverWithin 2" of Cover or Concealment
Stationary: +1D for In Cover Bonus.
Moving: No bonus, not exposed.Outside of 2" of Cover or Concealment
Stationary: Exposed. May get In Cover Bonus if QC is passed.
Moving: Exposed.Irregular ForcesIn Solid Cover
Stationary: +1D for Solid Cover, QC to get In Cover Bonus.
Moving: +1D for Solid Cover.Within 2" of Cover or Concealment
Stationary: QC to get In Cover Bonus.
Moving: Not Exposed.Outside of 2" of Cover or Concealment
Hopefully that helps!