Frozen like a hare in the headlights of a car

Do you know the meaning of: Frozen like a hare in the headlights of a car?

I've heard the expression -- deer in the headlights. It's literal. Deer do freeze -- don't move -- when they are caught by a car's headlights.

The usual phrase this (the European) side of the Atlantic is 'caught like a rabbit in the headlights' which means the same, but although I have often seen, in the headlights, rabbits running across or along roads I have never seen one freeze when thus caught.

DFG