Carnot cycle on the T-s diagram has two isentropes and two reversible isothermals. Why is it that the isentropes indicate a finite change in entropy?

For an irreversible process, the entropy will increase.
Hence removal of heat from the system (cooling) is necessary to maintain a constant internal entropy for an irreversible process in order to make it isentropic.
Thus an irreversible isentropic process is not adiabatic.