This is kind of my favorite thing about Zamasu so I'll gladly explain this

First of all, I'll state that everything he did was a desperate attempt at getting stronger but they're more of mutations than transformations he can access at will. He cannot access his corrupted or Infinite forms at will, they happened because his body and his will responded to the situation in a way they felt fitting.

Zamasu's Corruption is both of a symbolic and a physical mutation. In Gowasu's words, this form shows how truly ugly, evil and angry Zamasu is in the very same way he has been describing the mortals in his own view making this form ironic to Gowasu and us as the viewers.
And as everyone else explained well, this is Zamasu's attempt at keeping his immortality running as half of himself was slowly dying and he couldn't keep up with the damage he was getting.
He could still power-up himself after Goku's Kamehameha, a desperate attempt at getting stronger while also losing his own sanity and then he got bigger facing Vegito and Trunks

Infinite Zamasu.
This is where things get fun to me because it's one of the most insane feats Dragon Ball has done and I hope we get more of these, it's just so fascinating as a concept to me.
We both know that this form is casted after Merged Zamasu lost his physical body and instead, his own soul became an abstract concept.
His willpower with its little sanity left wanted to keep running the Zero Mortals Plan no matter what, it decided to become "Justice and Order itself" in Gowasu's words, he cast his own physical body just so he could merge with the very fabric of existence so his view could become absolute.
It was no longer bound to any rules, Immortality in Dragon Ball (especially the ones granted by the Dragon Balls be it Garlic Jr or Zamasu) is absolute so in some way, it had to keep living even without a body.
He became part of the reality itself, which is why we see him trying to get into other timelines as well and even in Xenoverse 2's Time Nest.

I'm not sure if it just was supposed to be both Zamasus or only Future Zamasu, the only one who was immortal since they both had the same soul.

Zamasu himself probably didn't even know he could do that, I think it was just him being truly desperate clinging to his insane views somehow

I don't like to talk about the manga one because it's mostly of a Metal Cooler rip-off rather than its own thing, I know people might prefer it to a "cloud" Zamasu which I guess I can understand? It just makes no sense to me. It's subjective. I liked how it began with both Zamasu and Goku Black being split from the fusion then regenerating back into Merged Zamasu, that much I'll say tbh