If my memory serves me correctly, the only "definition" truly used by the Appalachian Trail Conservancy is "2000 miler". someone who has hiked the entire trail. They do not make a distinction between those who section hike, those who walk the entire 2000+ miles with vehicle support, those who complete it in a year and stay in hotels every 5 or so days, those who hike half of it and then take a 3 month break and complete the other half within the same calendar year, etc...

I have heard some say all 2000 milers are section hikers, it is just a matter of how you connect each section and how long you are away from the trail between those sections. I agree with others, that you hike for your own reasons, and your own definition is what matters to you.