If I recall this was all covered in full in the HP&L section of the PPL exams. As I understood it at the time, both cases have the same issue at their heart, relative speed. The car going at the speed of light would initially see where it was going, but the light/space friction co efficient, or drag, means that within a period of time as the light lost energy and the car continued forward, there would come a point at which the car would have travelled further than the light. Effectively it would pass its own light ends, leaving them behind.
The bullet would be the same but the friction or drag would be greater as the mass of the bullet will be more than the mass of a photon. Initially the bullet would leave the gun, well, like a speeding bullet, but would lose energy quickly, whilst the car continued to speed along. Eventually the bullet would crash through the car window. This is exactly why the POH of all supersonic fighters require bullets to be fired at an airspeed slower than the muzzle velocity of the guns, or, for an immediate change of direction after firing. In other words a change in velocity.
A similar analogy which is easier to comprehend is the old adage, never pee into a head wind. Same thing really.
I hope that is clear.
