What exactly would make this "a true sequel" and not an expansion type of release for those who feel that way?
Good post, and to answer your question, here's what would make the game feel like a sequel to me:
-Longer story missions. I appreciate that Destiny has bite sized story missions because even though I enjoy a long campaign mission, I don't want to replay a longass mission for a daily story just to get loot. Yet there was always that nagging feeling with Destiny that the Story missions were insultingly short to the extent that I didn't care what was happening even when they started to improve the lore. It didn't feel like anything was unfolding because just as soon as you were thrust into action, you had won the battle and you were staring at your mission reward screen. That's obviously part of the Destiny formula that is unlikely to change, but I'd hope they look into the length of those missions to deliver a more meaty Campaign. I've replaced the first Felwinter's Peak mission in Rise of Iron more than any other in Destiny - of my own volition, mind you - because it feels more like a progressive story mission and less like a side quest.
-Transmog, or whatever it's called that let's you have more control over your Guardian's appearance. We got a little of this with infusion, chromas and ornaments, but Destiny customization - while there is plenty of armor by this time in Destiny 1 - still feels restricted. I honestly don't like the majority of the armor in the game, and the ones I do like are either low light or don't have any stats on them. This extends to the weapons as well; my favorite looking weapons in Destiny 1 were the white common gear and that was pretty much useless after playing for a few hours. Vanity is a big draw for me in any game, and it would feel like a true leap forward if this was addressed with Destiny 2. Like if the shader system is overhauled to apply to sections of gear rather than your entire Guardian, that would be a big bonus for me.
-New Enemy behaviors. Destiny already has several dozen enemies and I wasn't really expecting a completely new class of them. A new race with its own lore would definitely shake things up, but it's more important to me to see new AI behaviors. We're already seeing Psion and Minotaur snipers and some Centurions wielding blades and I'd like to see that extend throughout all ranks. When the Taken were introduced in Destiny 1, they felt like new enemies - even though they were literally reskins - because they behaved completely different. We're obviously annoyed at them by now so I hope they're nowhere to be found, but I'd hope Destiny 2 has something like that to prevent things from getting stale. This is especially important in boss battles, and I'd hope The Inverted Spire is not indicative of the furthest they attempted to deviate from Destiny 1's boss battle formula.
-Better Vehicles. This was the weakest area of Destiny's sandbox, such so that it felt like an afterthought. One could argue that Destiny doesn't need vehicles, but from developers who were arguably the best at them at one point, it was puzzling how little attention they received. I believe we've seen a drivable tank already so there are most likely a few new ones. But this is definitely one area they can really improve upon within the game - one that would make it feel like more than the past expansions.
-PvP customization. I've read that private matches wont be in the game at launch, which is whatever, but I'd hope that if (and hopefully
when) they arrive, there are more options for customization. Again, this is the former developer of Halo, so I want to see options that let players run around with Supers all game or have more control over gametypes and settings.
I'm not expecting a theater mode, a Forge, a decal editor, player trading, space ship combat or other things that could potentially make the game "not Destiny", but I wouldn't mind if they were there. Nevertheless, everything I've listed above builds on top of the game's existing systems and they're things I hope they have yet to show.
I'll probably think of more later.