If $F$ is a sheaf on usual Zariski site of an integral scheme $X$ (each $O_U(U)$ is a domain), then it is called torsion-free if $F(U)$ is torsion-free $O_U(U)$ module for every $U\in X_{Zar}$.
Now how to define a torsion-free sheaf on the small etale site of a integral scheme? The problem is unlike the Zariski case, $O_U(U)$ are not integral domains ( reduced but not irreducible/connected) when $U \in X_{et}$. Moreover, this also shows that even the structure sheaf for $X_{et}$ is not torsion-free.
So my first guess was to define $F$ in $X_{et}$ as torsion-free if $F|_{X_{zar}}$ is torsion-free. However, it seems to me that I am making some mistake.