Critical Conduction Mode is when you monitor the current in the inductor to keep its operation on the Boundary betwèen continuous and discontinuous. It's àlso know as Boundary conduction mode. It gives you a lot of the DCM benefits simpler control loop, smaller inductor, cheaper diodes.Continuous, Discontinuous, and Critical.
Continuous Conduction occurs when current never stops flowing through the inductor.
Discontinuous Conduction occurs when the inductor "runs dry" -that is current goes to zero during the switching cycle.
I'll wait for somebody else to answer about Critical Conduction mode.