The holographic sight also moves with your head. The reticle stays on target but moves around on the actual sight if you move your head side to side etc.
A holographic sight is a red dot type site, but uses an "open" design instead of a sealed tube.
Aimpoints do the same thing.
I believe the difference is simply in the method used to get the dot in front of your face.
Red dot (Aimpoint) is simply a red dot illuminated on the sight, usually in red and/or green. Holo sights (eotech) project a crosshair like image on the sight. Both have their advantages and disadvantages.
I have an Aimpoint M4. I love the 80,000 hour battery life on a single AA...plus they're dead nuts reliable. I leave mine turned on to the brightness setting I prefer.
Are the advantages/disadvantages the same on pistol as they are on a rifle? Are the same units just as good on pistols, or are there various models which are better on pistols than on rifles?