Connection between differential form of a manifold and Sheaf of relative differential of a map of schemes.

Question

I was wondering whether there is a connection between the differential form of a manifold and Sheaf of Relative differential of a Scheme map.

Definitions: Differential form on a manifold M is a map $\omega: M \rightarrow \sqcup _{p\in M}T_p^{*}(M)$ such that $\omega(p)\in T_p^{*}(M)$

Sheaf of differentials relative to a map $f:X\rightarrow Y$: There exists a unique quasi-coherent sheaf $\Omega_{X/Y}$ on X such that for any affine open subset $V$ of $Y$, any affine open subset $U$ of $f^{-1}(V)$, we have

$\Omega_{X/Y}|_{U}\cong(\Omega_{\mathcal O_{X}(U)/ {\mathcal O_{Y}}(V)})^{\sim}$