Separated means grade-separation, either elevated or underground. There is also at-grade seperation, which is what freight lines (and most light rail systems) use, railroad gates are used to provide time-separation where roads and railways intersect.
Exclusive means 'transit only', a prohibition enforced with physical separation, typically in the form of either a Jersey barrier or a curb.
Dedicated also means 'transit only', but without the physical separation of a barrier. Typically, this is what is used for bus-lanes. Lacking physical barriers preventing entry and exit, enforcing it is more difficult. It gets used because it is a) cheap, and b) emergency response agencies oppose physical barriers that limit their ability to make U-turns across streets.
Mixed is 'mixed traffic', where the transit vehicle operates like a private vehicle.