The Internet operates at near light speed, which on a planet the size of Earch often practically amounts to near real-time.
Digital information such as Internet packets travel at 2/3 of the speed of light on copper wire and on fiber optic cables. Since light speed is about 300,000 kilometers a second, this means digital communications travel at about 200,000 kilometers a second, slowing down only because because copper and fiber optic materials are about one-third thicker than a vacuum.
At this speed and neglecting switching delays, two computers have to be more than ten thousand kilometers apart, or almost half way around the world, before they experience a tenth of a second in communications delay.
With fixed near-optimal transmission speed, there are only two ways to make Internet networks faster -- increase the number of bits that are traveling at once down the connection, or increase the speed at which you switch them from one connection to another at the junction points.
Internet routers are getting faster and faster with switching speeds nearing instantaneous, while fiber optics and wireless technologies are enabling networks to send much larger numbers of bits at once. The Internet is getting even faster.
Thus what I understand from this is that yes as you said it is about 2/3 the speed of light, but Copper and Fibers have the same travel time. Fibre is only better in that you can send more data on them. (that is A LOT more!) Latency or Pings however will be the same with either, and will be slowed down due to switching and the actual travel distance.