A part played, with duties attached to the part rather than the person. A role can be left; the record of holding it stays.
Latin rotulus (a little wheel, a roll of paper), diminutive of rota (a wheel); an actor's part was once literally written on such a roll, and the paper's name became the part's name and then the standing of whoever held it.
A part played, carrying its own duties apart from whoever is currently playing it — a role can be set down, but the record of having held it does not go with it.