In this US generally red light running means entering the intersection AFTER the light has turned red. Enter point of intersection is usually the line drawn from curb to curb, which is beyond the white painted stop line. This varies state by state and of course has nothing to do with where you are. Anyway entering on yellow is never considered red light running as far as I know - maybe there are some places where you need to be cleared out of intersection when light turns red.
Slamming on the brakes for a yellow can be very dangerous.

Al