They aren't the same thing. Universities might have an "interest" in protecting students from online harassment. That doesn't mean a lawsuit alleging the university has a "duty" to protect students from online harassment has merit.
But, yes, Universities also have legal duties to their students. However, these vary significantly based on too many different factors to speak usefully in generalities (eg based on city & state, public or private, is it a research university, is there some kind of consent decree, etc) and of course, the facts of each case.
More simply: whether a University has a legal duty to protect students from online harassment will depend on the specific situation, but, in all cases, the University will have an interest.
I (for one) believe universities should not have a legal duty to prevent online harrassment, even though it may be of interest to universities.
I'm not arguing there is always a legal duty here, nor that there always should be. I'm stating that whether there is a duty will always depend on the individual fact pattern & the laws/regulations that apply to that specific University.
Not only do Universities operate under different jurisdictions with different rules & laws--but their level of "control, influence and involvement" varies along too. This changes what duty there is--as do the specific facts.So such generalizations are not applicable.
Hope this makes sense; its not easy to explain!