I guess the biggest difference is that bicycle touring you have anywhere from 2 to 6 bags on your bike instead of one bag on your back. Also the panniers (packs/saddlebags) are heavier: made from 1000 denier Cordura. Abrasion reisistence is far more important that lightwieght. Descending some mountain pass at 45 miles per hour is not the time for freakin silnylon bags, lol. If you fall your bags will disintegrate.
So you see, tourists tend to use heavier gear since the bike frame is hauling the weight instead of your back. Plus you're hauling six times as many bags. So you could haul a few more luxury items that you probably would on a hike.
Also, you'll cover more miles. Even averaging 8 miles per hour you'd be moving two or three times faster than a hiker. Most tourists do like 60 miles a day or what they call a Metric Century (100 kilometers). So at 60 miles a day, the Natchez Trace should be doable in a week's time.
Since you've got that kind of speed, there is no need to do all these complex mail drops and stuff. Just eat in town, local groceries and stuff.
As a southeasterner, stealth camping is the way to go. Plenty of trees down here. But make sure it isn't hunting season, or that you sneaking onto private lands. Lots of those lands are private hunting lands, be careful.
I plan to do the Section #1 of the new Underground Railroad Route hopefully next summer: http://www.adventurecycling.com/rout...?pg=detail&s=1
Here's a good book on bicycle touring: http://www.amazon.com/Essential-Tour...4959642&sr=8-1