When reading about contact geometry one quickly encounters the notion of a cooriented contact structure/form. But I do not seem to be able to find a definition of "coorientation".
In some places they define a cooriented contact structure as one induced by a globally defined 1-form, but in other places (such as wikipedia) they note that coorientation implies the global definition of the contact form.
Is there a general notion of coorientation on manifolds or distributions (on manifolds)? Is this related to the general notion of orientation of a manifold?