[Blaser]

On/off Contrast is the Ratio in brightness between maximum white and blackest black the projector can do at all. Native Contrast ratio is IMO the most important parameter of picture quality, the greater the difference, the better. Poor native contrast is synonymous of a washed out picture. Native contrast is illustrative of intra-image contrast and it is what we actually see.
On/off contrast is associated with the used of dynamic iris. Its effect is beneficial for dark pictures where it reduces the overall brightness leading to better blacks, but not contrast ratio! Go for the highest native contrast ratio producing machine you can afford for greater enjoyment!
Note: Screen reflective properties can raise or lower the perceived brightness, but there is no way they can do anything about contrast. It can increase the overall picture brightness so that both whites and blacks will be grighter, or vice versa. The use of a "high contrast grey" screen can be helpful with some ambient light, as blacks will be blacker and will apear less washed out. It helps "fool our brain" contrast is better, but again it will do nothing in reality to the native contrast ratio itself.