Neo4j Aura Professional
When you create a Professional AuraDB instance, the database user neo4j will be created by default for you. When you look at this user's detailed info, you will find out that this user has the role of PUBLIC; in Neo4j Aura Professional, the role of PUBLIC is an administrator role. Since Professional tier Aura instances do not have Role Based Access Control (RBAC), only the PUBLIC role exists (with administrator's privileges).
Neo4j Aura Enterprise
When you create an Enterprise AuraDB instance, the database user neo4j will be created for you. When you look at this user's detailed info, you will see this user has roles: admin and PUBLIC. If you want to understand more about these roles, you can find them and the related privileges on the Neo4j RBAC documentation page.
Note: Neo4j Aura Enterprise provides Role Based Access Control (RBAC). Please refer to Neo4j RBAC documentation for more detailed information including a complete list of pre-defined roles and related privileges.