# Different almost complex structures

I think I am confused about some definitions involving equivalence of almost complex structures.

Is it true that given an almost complex structure on a manifold, there is at most one complex structure that realizes it? This seems to be true but I am not completely sure.

Also, I know that there is a whole moduli space of complex structures on a surface. If I have two inequivalent complex structures on a surface, does this imply that the almost complex structures are also not equivalent? In particular, is there a moduli space of almost complex structures? Somehow I thought all almost complex structures were equivalent since almost complex structures are a topological as opposed to geometric notion.

See my related question: Space of smooth structures

Hint: Suppose that $M, M'$ are complex manifolds; let $J, J'$ denote their respective almost complex structures. Let $f: M\to M'$ be a diffeomorphism such that $f_*(J)=J'$. Show that $f$ is complex-differentiable and, hence, biholomorphic. If it helps, start with the case of complex dimension 1. If it does not help, see this wikipedia article.