Understanding the different filtration processes between bourbon and Tennessee whiskey is understanding why Tennessee whiskey is not legally considered bourbon. Because products like Jack Daniel's and George Dickel use the "Lincoln County Process," they are technically not bourbons.
The Lincoln County Process is not a new thing. It got its name because Jack Daniel's Lynchburg, TN distillery was in Lincoln County before county boundaries were reassigned (Daniel's is now in Moore County). But, before it was called such, it was a practice used by many whiskey rectifiers to improve the often-times harsh taste of the unaged whiskey sold in the 19th century. The process, also known as charcoal mellowing or leaching, is one by which whiskey is filtered before it goes into the barrel. Here's how it goes:
Sugar maple trees are harvested in the fall, when the trees' sap content is low, and are then air dried and cut into 5 foot long boards. The boards are stacked crosswise on top of each other, like a lattice, until the pile reaches about 7 feet tall. These piles are called ricks. The ricks are then set ablaze while men with water hoses control the temperature - to high a temperature would reduce the maple to ash, instead of charcoal. Once all the wood is burned to charcoal, the charcoal pieces are dumped into a vat that's between 8 and 10 feet tall, creating a column of charcoal. Then in goes the unaged whiskey where it drips and filters through the charcoal column and out the bottom of the vat through a wool blanket. It takes a week to 10 days to complete its course through the charcoal. From there, the charcoal filtered whiskey goes into the barrel to age.
The effect of the charcoal filtering gives the whiskey a sooty characteristic (celebrated by Jack Daniel's fans) and gives the whiskey a distinct smoothness. Charcoal filtering also jump-starts the aging process by subjecting the green whiskey to the benefits of charred wood. You see, when whiskey is aging in its charred oak barrel, the chemical interactions between the wood and the liquid reduce the undesireable cogeners. Cogeners are fusel oils and acids that are naturally created during distillation. They are what give unaged, raw whiskey its awful taste. So, giving the whiskey time to flow in and out of charred barrel allows science to do its work, and blunt the offensive tastes by removing the cogeners. (Keep in mind that not all cogeners are "bad;" while some are toxic in high concentration, some are harmless and even add to the character and body of bourbons). So, filtering the new whiskey in the Lincoln County Process gives the mellowing abilities of the charcoal a head start before it's times for barrel aging.
Boubon is also filtered, but in a very different manner from Tennessee whiskey. The filtration of bourbon is largely a 20th century practice. It happens after bourbon has been aged, but before it's bottled, and has only cosmetic purposes. When bourbon is done aging, it has in it some harmless impurities. These impurities are naturally occurring fatty acids and proteins, and are the reason behind the dreaded chill haze - the cloudiness that appears in bourbon when it's chilled. Since consumers think this cloudiness is a sign of bad bourbon, distillers filter the impurities out. Again, it's merely for appearance, and some bourbon enthusiasts think the removal of these impurities removes some of the subtle tastes from their drinks. So, to appease their drinking public, distillers chill their bourbon before it's bottled and filter out the particulates. The bourbon is chilled for filtration because it makes the impurities easier to find and remove. If you haven't done so already, try some Booker's which isn't filtered at all.
Now, there is some debate about the real difference between bourbon and Tennessee whiskey. The two differ only in that Tennessee whiskey undergoes the Lincoln County Process - it has an added filtration step. However, Jack Daniel's and George Dickel, which are the only two Tennessee whiskies, meet all the legal requirements of bourbon set forth by the Federal Regulations. So, where is the real difference? Technically, any bourbon could be charcoal filtered and still legally be called a bourbon. I suppose those that enjoy debating these types of things will comment on the taste differences between the two: charcoal filtering takes away too much taste, charcoal filtering adds too much taste, charcoal filtering makes it too sooty.... Whatever side of the fence, nay rick, you are on, my suggestion is to drink what you enjoy and let labels be labels.