Camping is fairly luxirious compared to backpacking. Backpacking is carrying everything you need to survive on your back. I typically do 5-7days for long trips, but people do months as well. There is also the weekend warriors - which is kind of what we (the group as a whole) do - who just go out for a 3day 2night trip. But backpacking means no showers, ice cold drinks (unless you are bping in a cold climate), restrooms, or comfortable accomodations (the more stuff you put in your backpack, the heavier it is going to be). But the pay off is far better than camping.
Backpackers checklist (10 essentials):
http://www.backpacking.net/Jims-10-Essentials.html
When camping, the attraction is a view of something grand - such as mountains or a canyon. Backpacking is being out in that view - in those mountains or canyons. Seeing them first person instead of third person.