Given a graded ring S and a graded S-module we can carry out a construction in order to get , 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 of rank 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 then the sheaf is locally free? If so, I can get from a locally free sheaf 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.