There shouldn't be any major changes to the game in the near term. Bungie plans to maintain the existing Destiny roadmap, including seasonal events.
It's not clear what prompted the shift, but it's not surprising that either side would be happy with the deal. Activision hasn't been shy about its disappointment with Destiny 2's sales (regardless of how strong they actually are), and has taken to offering the core games for free to PS4 and PC gamers through temporary promos. This eliminates financial risks if Destiny runs into further trouble. Bungie, meanwhile, can preserve its vision for the franchise -- unlike with Halo, it doesn't have to worry about a publisher taking things in a different direction.
It's not certain what this means for Destiny in the long run. The loot box-style engrams and microtransactions aren't necessarily going to go away just because Activision isn't involved. And like it or not, paid add-ons like Forsaken's Annual Pass are commonplace in gaming, not just in titles from big publishers. Still, don't be shocked if there's a significant change in Destiny's course over the years ahead.