The definition of done applies to the scrum team during the course of a project. The definition is applied to every story as a way of determining if the story is finished. You won't have a different definition of done for each story, that's what acceptance criteria is for.
It typically exists for the life of a project, but as with all things scrum, the team ...
In the November 2017 edition of the Scrum Guide, it states that:
When a Product Backlog item or an Increment is described as "Done",
everyone must understand what "Done" means. Although this may vary
significantly per Scrum Team, members must have a shared understanding
of what it means for work to be complete, to ensure transparency. ...