Acting President = someone legally exercising full presidential powers despite not legally holding the office. Acting President can either serve as a stand-in (with Actual President incapacitated) or during vacancy (some argue that a Speaker replacing President would formally be "Acting President").
I would imagine that a Speaker holding the office for the balance of a term would probably be able to extend the constitutional convention set by Tyler to his or her own situation, on the grounds Inks stated.
