Research has usually considered cyberbullying as a unitary phenomenon. Thus, it has been neglected to explore whether the specific online aggressive behaviours relate differentially to demographic features of the perpetrators of online aggressive actions, their personality characteristics, or to the ways in which they interact with the Internet. To bridge this gap, a study was conducted through a questionnaire administered online to 1228 Italian high-school students (Female: 61.1%; 14-15 yo: 48.%; 16-17 yo: 29.1%; 18-20 yo: 20.4%, 21-25 yo: 1.6%; Northern Italy: 4.1%; Central Italy: 59.2%; Southern Italy: 36.4%). The questionnaire, in addition to items about the use of social media, mechanisms of Moral Disengagement and personality characteristics of the participants in the study, also included a scale for the measurement of cyberbullying through the reference to six aggressive behaviours. The results indicate that cyberbullying can be considered as a non-unitary phenomenon in which the different aggressive behaviours can be related to different individual characteristics such as gender, personality traits and the different ways of interacting with social media. Moreover, the existence of two components of cyberbullying has been highlighted, one related to virtual offensive actions directly aimed at a victim, the other to indirect actions, more likely conducted involving bystanders. These findings open important perspectives for understanding, preventing, and mitigating cyberbullying among adolescents.