I see public relations and public engagement as going together but serving two very different purposes. Public relations focuses on how the school communicates information, including social media posts, newsletters, school board information, and newspaper articles recognizing the accomplishments of both staff and students.
To me public engagement is taking that communication futher by creating opportunities to for patrons to see you in public. To me this looks like attending athletic events, activities, and community events. The most important asset that families have is their children and showing support for those kids is a great opportunity for the community to not only see you but interact with you. I also think as part of this it's important to attend other community events such as festivals and community meetings to learn and hear what the community needs and how the school is perceived.
Public engagement requires a superintendent to build relationships so when the school needs the support of the community that it is in that support is there for the school system. Public Relations can also help with this as the community will be receiving information about the happenings at school and feel informed of what is happening on a daily and weekly basis.