For more than a decade the continuous membrane column (CMC) has been touted as being a revolutionary separation device since it is capable of producing a highly enriched product without cascading. Most studies have ignored membrane cascades in favor of the one-compressor permeator (OCP) designs, implying that a CMC or one of the other OCPs is always more efficient than multi-compressor cascades. Moreover, it has been claimed that a CMC is completely analogous to a packed distillation column, and the design and performance of CMCs have been analyzed in terms of concepts developed for equilibrium processes. This paper shows how basic separation science and cascade theory applies both to membrane permeation and distillation, and shows that a CMC cannot be analogous to distillation because the recycle flow pattern in distillation is characteristic of that in a countercurrent recycle cascade (CRC), while it is not in a CMC. On the other hand, a number of membrane permeators can be connected in series to form the recycle flow pattern of a CRC. A theoretical comparison of the performance of ideal CMCs with membrane CRCs provides an insight as to why some of the one-compressor permeator designs require much larger membrane areas and compressor duties than that required by CRCs to obtain the same separation. Although the enrichment that occurs in a CMC is increased with increasing recycle rate similar to that in a CRC, the mechanism is entirely different in the two designs. It is suggested that a CMC and some of the other OCPs are single permeation stages with enrichment that depends both on recycle rate and cut. The consequences of some of the thermodynamic distinctions between the rate-governed permeation and equilibrium processes such as distillation are briefly explored.