Basically TN has 3 classes (A, AA, AAA), but for the football playoffs, they are split into six (A: 1A & 2A; AA: 3A & 4A; AAA: 5A & 6A).
D1 and D2 are for private schools that allow students who receive financial aid to play sports. Private schools like Lipscomb and Knoxville Catholic, for example, are private schools yet play on the public side. The downside for those schools is that TSSAA uses a very unfair (IMO) multiplier for privates in the public league, 1.7. Catholic has like 600 kids yet will be grouped with public schools with enrollments ranging from 1500-2000. The high multiplier (again, IMO) is a consequence of Brentwood Academy's long standing issues with TSSAA. BA is a small private school that recruits Nashville so hard they are practically a Junior College. They previously competed in the highest class (before the public/private split) and won state every year in football. TSSAA took exception to all of this and split them up. They are going to make it an uphill battle for any private school that wants to compete in the public league, even if those schools don't allow student athletes getting assistance to play athletics.
You can downplay it off all you want, but if its recruiting, its recruiting. There's no reason a public school should be allowed to have a handful of players who don't even live in the county to (supposedly) pay a tuition and play in the public league under the current rules.