Projects are the basic organizational element in Mantis. Users are assigned access and roles by project.
Sub-projects are projects in their own right. A sub-project be attached to multiple parent projects. For example, a common utility library can be represented as a sub-project. For searches or reporting, the issues in sub-projects are combined with those of the parent project, i.e. issues of the sub-projects are shown when visualizing those from the parent project. The sub-project can also have different team members than the parent project.
Categories are used within projects to separate issues into smaller groups. New issues in each category can be assigned to an individual team member by default.