In the definition of isotropic and Lagrangian submanifolds of a symplectic manifold, it seems that there are two equivalent definitions.
The symplectic two-form annihilates tangent vectors (denoted $T_i$) of the submanifold $\gamma$, i.e., \begin{equation} \omega(T_1,T_2)=0. \end{equation}
The restriction of the two-form to the submanifold, $\gamma$ vanishes. \begin{equation} \omega|_{\gamma}=0. \end{equation}
Why are these two definitions equivalent, and does such an equivalence hold for any two-form?