Definition of stalks of etale sheaves.

Question

Let $\bar{x} \longmapsto X$ be a geometric point of a scheme. Let $G$ be a sheaf on $X_{et}$. Then there are two definitions of the stalks: $G_{\bar{x}} = i^{*}G(\bar{x}) $ and $\varinjlim_{U,i_{u}}G(U)$, where $(U,i_{u})$ is an etale neighborhood of $\bar{x}$. How do these two definitions coincide? The problem is that in case of $i^{*}G(\bar{x})$ we need to also sheafify.