Continuity is a kind of change, not a synonym for staying the same.

Evidence

Continuity can denote change; however, a particular sort of change that occurs in non-disruptive manner. The change involved in continuity is not necessarily small, but it happens without ruptures that disconnect the new situation from the past. The outcome of change has enough similarity with history to be recognized as its continuous follower. … In this sense, a development is not continuous or discontinuous per se. Continuity is ascribed to a process by those interpreting it. — Georg Schreyögg and Jörg Sydow, The Hidden Dynamics of Path Dependence, 505

Categorization

• DEFINE: Separates continuity from stability: continuity permits large change provided no rupture disconnects present from past.
• APHORISMS: Usable in practice: judge a change by whether it can be recognized as a continuous follower of what came before — a test for reform that preserves identity.