Basic question about isomorphism of $O_X$-modules.

Question

Let $X$ be a scheme. Suppose I have two $O_X$-modules $F$ and $G$ and a homomorphism $\psi: F \to G$. As sheaves of rings on $X$ we know that $\psi$ is an isomorphism if and only if $\psi_x: F_x \to G_x$ is an isomorphism. What is the equivalent statement if I want $\psi$ to be an isomorphism of $O_X$-modules? Thank you.