I guess the underlying source of confusion is that they're both measures of severity, but priority is severity from business viewpoint while severity is severity from the affected user's viewpoint.
A high priority bug that isn't fixed presumably has severe consequences for business (or it was prioritized wrong).
A high severity bug that isn't prioritized presumably has low consequences (severity) for business, but it probably really sucks for the unfortunate user who is affected.
A high priority bug that isn't fixed presumably has severe consequences for business (or it was prioritized wrong).
A high severity bug that isn't prioritized presumably has low consequences (severity) for business, but it probably really sucks for the unfortunate user who is affected.