If they use the word edition, it will almost certainly be just "Anniversary Edition." They might go with Revised Dungeon & Dragons, but I find that unlikely.
It really comes down to how you define an edition. We are currently playing the 5th edition of Dungeons & Dragons. You have: OD&D, BECMI, 3E, 4E, and now 5E, as technically Advanced Dungeons & Dragons was a different game. If you want to break things down by major rule changes across all Dungeons & Dragons, it gets messy.
- OD&D: 1-4 versions
- At least Greyhawk made significant changes, and I believe the other supplements might have as well
- 1E AD&D: 2 versions
- Unearthed Arcana made changes enough to be considered 1.5E
- BECMI: 2-6 versions
- Each set made significant changes, but arguably they were extensions of the rules like OD&D had. The Rules Compendium combined them all, which I'd consider a half edition at least
- 2E AD&D: 2 versions
- The revised version would have been a half edition
- 3E : 2 versions
- Everyone knows the half edition
- 4E: 2 versions
- The Essentials set was a half edition change
- 5E: 1 version (plus probably 1 in 2024)
So at a minimum we've had 12 major rule systems, and at most 19 versions. The fact that there's some compatibility might be irrelevant, since a lot of material from BECMI, 1E, and 2E was usable in any of these editions.