This is an honest question. I know light travels in a certain rate of speed, example turning a light on in a room but, when you turn the light off does the extinguished light travel at the same speed or do you measure the speed of the darkness?

There is no such thing as the "speed of darkness." However, there is a finite speed to the very last photon that is emitted by the light when you turn it off, and after that photon has passed then you have darkness. The speed of that last photon is, of course, c.

However, what you perceive as a lit room is the result of photons bouncing off surfaces and into your eye. So after that last photon goes whizzing byyou it may very well bounce off an object in the room and come back to your eye - consequently you have to take into acount the various paths that light can take as it travels from the light source to the objects in the room, bounces off them, and comes to you.