Since the first evidence for cancer stem cells in leukemia, experimentalists have sought to identify tumorigenic subpopulations in solid tumors. In parallel, scientists have argued over the implications of the existence of this subpopulation. On one side, the cancer stem cell hypothesis posits that a small subset of cells within a tumor are responsible for tumorigenesis and are capable of recapitulating the entire tumor on their own. Under this hypothesis, a tumor may be conceptualized as a series of coupled compartments, representing populations of progressively differentiated cell types, starting from stem cells. The allure of this model is that it elegantly explains our therapeutic failures: we have been targeting the wrong cells. Alternatively, the stochastic model states that all cells in a tumor can have stem-like properties, and have an equally small capability of forming a tumor. As tumors are, by nature, heterogeneous, there is ample evidence to support both hypotheses. We propose a mechanistic mathematical description that integrates these two theories, settling the dissonance between the schools of thought and providing a road map for integrating disparate experimental results into a single theoretical framework. We present experimental results from clonogenic assays that demonstrate the importance of defining this novel formulation, and the clarity that is provided when interpreting these results through the lens of this formulation.