I don't think so: the difference is that the crybully wants to silence his opponent, while the one using the term wants his opponent to stop silencing him. I.e., one wants to suppress liberty and one wants to preserve it.
I have no problem with your right to say that I'm wrong, or odious, or that my speech is completely offensive and inimical (although of course I disagree): where I draw the line is if you attempt to silence me altogether.