Quasi-Coherent Modules over a Ringed Space : Let $(X,\mathcal O_X)$ be a ringed space. A sheaf of modules $F$ over $(X,\mathcal O_X)$ is called quasi-coherent if for every point $x\in X$ $\exists U\subset X$ s.t ${F_{|}}_{U}$ is the cokernel of a map $\oplus_{i\in I}\mathcal O_U\rightarrow\oplus_{j\in J}\mathcal O_U$
Quasi-Coherent Modules over a Scheme: Let $(X,\mathcal O_X)$ be a Scheme. A sheaf of modules $F$ over $(X,\mathcal O_X)$ is called quasi-coherent if X can be covered by open affine subsets $U_i=Spec(A_i)$, such that for each $i$ there is an $A_i$ module $M_i$ with ${F_{|}}_{U_i}=\tilde{M_i}$
Question: How can one deduce the definition of quasi-coherent sheaf of module over a scheme from the definition of quasi-coherent sheaf of modules over a ringed space?