Cell populations of solid cancers and their distant models, the cancer cell lines, have been categorized in sub-populations: cancer stem–tumor-propagating cells (CSC–TPC) versus derived cells, epithelial-versus mesenchymal-type cells, dormant versus actively proliferating cells and so on. CSC–TPC are minimally defined by their operational properties: immortality and the ability to regenerate in vivo or in vitro the whole panel of cancer cells. The epithelial-to-mesenchymal transition (EMT), mostly observed in vitro, generates mesenchymal-type from epithelial-type cells. The converse transition is mesenchymal-to-epithelial transition. In vitro work suggests that CSC–TPC and EMT cell phenotypes overlap. An analysis of the properties of these sub-populations, as studied in vitro, shows that indeed these two phenotypes may be linked to some extent. However, the in vivo counterpart of this relation in human tumors has barely been investigated. A model in which among the EMT cells released from the tumor only the most competent CSC–TPC will succeed to metastasize is proposed. It is suggested that in the Darwinian evolution of cancer cells, many phenotypes reflecting the expression of various programs, reversible to irreversible, exclusive, overlapping or linked coexist and compete with each other.