What is the term "Red Band Clip" supposed to refer too and where does it come from?

I know that when movie trailers are shown in theaters, the red band trailers are shown in "R" rated movies and the rating is shown in red instead of the usual green.

This is because there is usually foul language and graphic content like sex or violence in the red band clip.

But I have no idea why its red.

When you go to the movies, you will see trailers with a big green slide that says "Approved for all audiences" before the trailer actually begins.

When trailers feature adult content (violence, sex, swearing), they have a red logo in front of them. You will very rarely ever see a red band trailer in the theaters, and if you do it will be with a Rated R film.

Anyway, the term red band is used to denote a clip that has content in it that would be the equivalent of an R rating.