The holding of a thread unbroken across change. Continuity is what makes a later moment belong to the same story as an earlier one.
Latin continuitas (uninterrupted connection), from continuus (unbroken, continuous), from continere (to hold together); the holding of a thread unbroken across change, so a later moment still belongs to the earlier story.
Latin continere is to hold together, and continuity is that grip extended through time rather than through space. Break the hold and two moments stop belonging to one story.