I'm pretty sure those were the only two. I'm also of the opinion that unless the elements that you have in a game are used frequently and have clear direct uses and counters, I'm all fine for them being make into generic non-elemental magic damage.
- Ice as cold damage & Fire as heat damage.
- Lightning vs. flying & machines & Earth vs. grounded & soft opponents.
- Poison vs. Healing
- Life vs. Death
Those are pretty easy to understand in terms of game mechanics and let you guess when they'll be effective.
As elemental damage sources, Water & Wind get awkward, because they're like a less scary Ice & Lightning respectively. Also Water damages machines, but also drowns breathing things, so it's not really clear when it works or when it doesn't. Wind is another one that's curious if it's effective against breathing things or not. I think that that's why they have the largest tendency to be implemented a tiny bit, but massively under utilized because it isn't easy to know what to expect from them in game mechanics.
Most often you want things that are visually clear and have obvious direct uses & opposing counters for elements in magic systems.
Given that approach, it'll be interesting to see how they differentiate other summons later on since they're pretty much all about big elemental-specific damage, but I think that the way they sort of join your party, and how they have variable interactions before their big attack will let them have room to be more than just their elemental natures.
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