Given a graded ring S and a graded S-module ![M](http://latex.mathoverflow.net/png?M) we can carry out a construction in order to get ![\tilde{M}](http://latex.mathoverflow.net/png?%5Ctilde%7BM%7D), which is a sheaf over the scheme Proj S. With this in view, I have an equivalence of categories between the category of (quasi-finite generate) modules and the category of q-coherent sheaves over Proj S. 

On the other hand, given a locally free sheaf ![\mathcal{F}](http://latex.mathoverflow.net/png?%5Cmathcal%7BF%7D) of rank ![n](http://latex.mathoverflow.net/png?n) over Proj S we can get a vector bundle out of it and further we have a 1-1 correspondence between isomorphism classes of free sheaves of rank n and isomorphism classes of vector bundles of rank n.

With the last two facts in view, my question is the following. if I start with a finite generated module ![M](http://latex.mathoverflow.net/png?M) then the sheaf ![\tilde{M}](http://latex.mathoverflow.net/png?%5Ctilde%7BM%7D) is locally free? If so, I can get from ![M](http://latex.mathoverflow.net/png?M) a locally free sheaf ![\tilde{M}](http://latex.mathoverflow.net/png?%5Ctilde%7BM%7D) and from such a sheaf a vector bundle (and perhaps backwards as well). Therefore, Is it the same having a vector bundle over Proj S than a S-Module? or what are the limits of such a relation described here among Vector Bundles & S-Modules?. By "Is it the same" I mean, We have the same amount of information in such objects.