Rollover is a process that creates a new, hidden copy of your existing module for use in a new academic period. The majority of content you used in the current year is included in the rolled-over copy (with the exception of student data, work done in activities like Forums and Turnitin assignments).
By contrast, a New Module Request will create a totally new Moodle page for the module or purpose concerned. This new page will largely be blank, aside from some basic template structure and will be hidden from other users. This allows you to start developing your module from new.