To clarify my own post... Three of the people who summoned Zoidark are still alive as of the start of Shadowbringers. Emet-Selch, Lahabrea, and Elidibus. They were part of the Convocation of Thirteen that came up with Zoidark's concept and summoned him with aether donated to them by half of the surviving Ancient population. So somehow, the people who summoned Zoidark all survived summoning him. This confirms it is possible to create a concept and use aether other then the concept creator's aether to fuel it. It also means the Ascians can tell us what the Concept behind Zoidark is since... they're actually alive to explain it to us. And they could all be Tempered by him.

None of the people who summoned Hydaelyn live past her summoning. All their aether went into fueling the concept they came up with. Unlike with Zoidark, no one is around to tell us what the Concept behind Hydaelyn actually is. The best everyone has been able to do is guess what Hydaelyn's Concept is, based on what they saw her do (fight Zoidark, Sunder him and the Star, become the new will of the Star). The death of Hydaelyn's Summoners also means they would have been dead long before Hydaelyn would be able to Temper them (if Hydaelyn can in fact do that).


Tangential to all of that is what we have known for a long time about Primal Summoning, particularly since HW. The "will" behind the people involved in summoning a Primal effects what that Primal is like. Titan summoned by the Kobalds collectively has different motivations then Titan summoned by just Ga Bu. And both of those are based on the same Concept, it's just two different versions of it. However, both versions are just as much the "Titan" Concept as the the other version is. Even the Ancients themselves tell us how getting distracted while Creating a Concept can change what that concept is like (Creating a Lion and getting distracted by a Hawk gives the Lion Concept hawk wings.).

So you've got Zoidark, the Concept. Which is getting summoned by people who have watched their entire world be destroyed around them by their nightmares come to life through their own Creation Magics. And they're using the aether of a population that has also gone through that. I think it's very probable that the Zoidark Concept gets... distorted by all the fears and desires of the people summoning it to be not quite what they planned the Concept to be. Kind like how you can have two primal Titans that are both Titan, with different motivations.

Hydaelyn's summoning conditions are a lot more stable then Zoidark's are. Or at least, the state of the Star is a lot more stable. By the time Hydaelyn is summoned, Zoidark has stopped the Calamity and rejuvenated the Star. Hydaelyn is Created in an environment that is most likely a lot less... frantic... then the one Zoidark was Created in. Zoidark was summoned to fix the Star right now. Hydaelyn was summoned to mitigate a problem that could happen in the future. And Hydaelyn is ultimately summoned for much more philosophical reasons then Zoidark was summoned.