Typical scenarios for rear-ends are a sudden deceleration by the first car (for example, to avoid someone crossing the street), and a following car that does not have the time to brake and impacts the first.
In rear-ends, mechanical damage is usually equally shared by the two vehicles (but this can change if vehicle masses were very different, see below). Injuries to the occupants are usually much worse for the impacted vehicle, because occupants of the following vehicle could see the imminent impact and could take measures against it.
As a rule of thumb, impacting into another car is equivalent to impacting into a rigid surface (like a wall) at half of the speed. This means that rear-ending a still car while going at 30 mph is equivalent, in terms of mechanical damage and occupants injury, to impacting a wall at 15 mph. The same is true for the impacted vehicle. This statement is true if the two vehicles have roughly the same mass. If, instead, one is much more massive than the other, the less massive suffers most of the consequences.
A typical medical consequence of rear-ends, even in case of collisions at moderate speed, is whiplash.