The main difference between bourbon and Tennessee whiskey lies in the Lincoln County Process, a form of charcoal filtration. In the 1820s someone (possibly Alfred Eaton) started filtering whiskey through maple charcoal. Tennessee whiskeys are now filtered through 10-12 feet of maple charcoal before they are bottled, removing impurities and giving a 'sooty' sweetness to the finished spirit.
A Tennessee whiskey must be made from at least 51% of one particular grain. This could be rye or wheat, but most often, as with bourbon, corn is the favoured base.