The only difference is the spelling and ages of those involved.
Truth be told we use the word "bullying" when it's done to kids/teens and we call it "harassment" when it's done to adults, especially in the workplace. If a teenage boy slaps his girlfriend we don't call it "domestic violence". If they were adults we would.
In past eras a certain amount of "bullying" was expected or tolerated in school. Some parents would teach their children how to fight back or defend themselves against bullies rather than have meetings with school officials. They looked at their children being bullied as a "teaching moment" or an opportunity for them to learn to stand up for themselves. Many parents believed overtime bullies would grow out of it or befriend the kids they terrorized. If it was really bad they'd transfer their child to a different school.
Today bullying is on a whole new level with the advent of the Internet, Twitter, YouTube, and Facebook. Simply switching schools is not going to offer a "fresh start". This has led to many young people committing suicide. They don't see an end in sight.
When it comes to adults people who are "harassed" oftentimes launch law suits against not only those that harassed them but anyone who is in a supervisor role that condoned the behavior or refused to help and sometimes the company itself held liable.