"Wait for green light" would suggest Westbound traffic gets a left turn arrow before Eastbound traffic gets their green light. Eastbound drivers need to wait for the green light, and not drive into the intersection if they see Westbound traffic start to move. This is a common sign at many intersections with left turn arrows.
Turning right on red requires a driver to stop, check for other vehicles and pedestrians, then turn if it is safe to do so.