The clear difference between harassment and bullying is harassment is ILLEGAL and bullying IS NOT. However, bullying is never acceptable and anyone bullying should be punished appropriately.

Harassment is aggressive pressure or intimidation which can make you feel intimidated. E.g. comments, jokes, gestures. Section 1 and 2 of the Protection from Harassment Act 1997 act defines acts of harassment.

Bullying has no legal definition but can be defined as very similar to harassment, it is not targeting a protected characteristic.