It's quite a common practice in agile or scrum teams to have a Definition of Done. However many teams (especially project teams in larger organizations) define their DoD in their 'political' context within their boundaries of control. This probably makes sense but often these DoD are not "complete" enough to immediately offer the completed stories to the customers. And that is why extra statuses or definitions of done are created and why terms like 'done done’, 'really done' exist. I've created another one: DoRR
Definition of Ready for Release; it helped me a lot in bigger projects in complex corporate environments where the DoD of the agile teams was not sufficient.
More details on our company blog: http://www.pmscrum.com/blog/2011/06/dorr-definition-ready-release