I would think it may hurt just a little bit more, for a child that is, to be intentionally hurt via the internet.
On a playground if someone calls you fat, you can stick out your tongue, tell them to shut up, or possibly give them a boxing lesson... They haven't learned yet to click ignore or better yet shut the darned thing off. Usually on the internet no one is standing there to observe the happenings and things can get out of control quickly.
On a playground, there is usually a teacher or play ground monitor that they can run to and say "So and so said this", the role of adults in a child's world is so entirely important! We teach them to ignore or walk away from verbal bullies.
Sitting on a computer, alone they learn to internalize and if they are repeatedly insulted can possibly come to believe it, damaging their psyche.