Ala-damn-bama Criminal Tide without a doubt, no question, no other even comes close!
I'm 62, the young pups haven't lived long enough to understand.
No other Volunteer rivalry has a name, "The Third Saturday in October". There used to be the "Beer Barrel" with Kentucky but the name was deemed inappropriate and was ended in 1999 by the Kentucky AD CM Newton after a deadly car crash involving drunken Kentucky players.
In the early 1900's Alabama was a powerhouse with national recognition. Tennessee was not and had no recognition, and was usually owned by Bama until Neyland beat them in 1928.
That game thrust Tennessee into the national spotlight on a regular basis for the first time. That is the year the game was given a name, and it has meaning to the players and fans (who get it). Not named after an object, but the day every year the competition will be held to determine the winner. This rivalry has always been owned by one or the other team in streaks. Like it is now by Bama but that will change. It ought to be a National Holiday.
Florida, Vanderbilt, Georgia, nor South Carolina, (Auburn should have been on the list indicating the OP doesn't get it) games have no name. They are ALL merely and only tough games in the SEC with nothing approaching the history, tradition, national following and recognition, game art, plethora of books written, internet links, and etc. ad nauseum.
No little ones ... Alabama is Tennessee's measuring stick when the Crimson is good, and Tennessee is Alabama's when the VOLS Rise to the TOP. Some day maybe you'll get it if you can get your nose out of Need for Speed-Most Wanted and participate in real life.
This from a BAMA site.
Alabama vs Tennessee: A Historical Retrospective - Roll 'Bama Roll
And of course Auburn, their in-state rival is their Alabama's biggest game. Then Tennessee, then LSU.
For me, ALA-Damn-BAMA, Vanderbilt (In-state), Florida, Georgia, Auburn, Kentucky -- in that order.