You're discounting the possibility that there's a difference. There's varying levels of harassment, and it should be up to the victim's discretion as to how severely it should be treated. If person A calls person B a jerk on Twitter, that's easily enough ignored (unless there's a pre-existing personal or parasocial relationship between persons A and B that would make "jerk" sting more than it otherwise would), but if person A organizes a campaign involving all of their followers whose sole intent is to make person B feel threatened then that's an entirely different matter.

The hardest part of dealing with online harassment and "trolls" seems to be drawing that line, or even acknowledging that it exists.