First of all, bourbon doesn't need to be made in Kentucky; there are bourbons on the market from Virginia and Indiana for instance. It DOES have to be made in the US though. Mash needs to have a corn content of between 51% and 80% (higher than 80% and it is a corn whiskey). Finally, it needs to mature in freshly-charred barrels. If it is matured in barrels which have already been used for bourbon maturation it's not a bourbon. For instance, 'Early Times' in some markets is a 'Kentucky Whiskey', not a bourbon.
The big thing that differentiates a Tennessee whiskey from a bourbon is the filtering through a thick layer of charcoal. On top of that, it also has to be made in Tennessee. Besides JD, the other Tennessee whiskey distillery operating at the moment is George Dickel.
Hope this answers your questions!