  We show that the category of affine bundles over a smooth manifold M is
equivalent to the category of affine spaces modelled on projective finitely
generated C^\infty(M)-modules. Using this equivalence of categories, we are
able to give an alternate proof of the main result of [13], showing that the
characterization of vector bundles by means of their Lie algebras of
homogeneous differential operators also holds for vector bundles of rank 1 and
over any base manifolds.
