Your car radiator is actually using convection to convect heat into the air.

The spacecraft radiators use radiation to dump heat by emitting infrared photons. Photons do not require a medium. This type of radiator works by maximizing the area of hot surface exposed to empty space (which has an effective temperature of 3 K). They have to be pointed into a dark area and away from the sun. There’s no advantage to fins, because you want to maximize area perpendicular to the dark sky.

Both devices are called radiators, but they are different kinds of devices.