Adult stem cells (ASCs) in vertebrates and model invertebrates (e.g. Drosophila melanogaster) are typically long‐lived, lineage‐restricted, clonogenic and quiescent cells with somatic descendants and tissue/organ‐restricted activities. Such ASCs are mostly rare, morphologically undifferentiated, and undergo asymmetric cell division. Characterized by ‘stemness’ gene expression, they can regulate tissue/organ homeostasis, repair and regeneration. By contrast, analysis of other animal phyla shows that ASCs emerge at different life stages, present both differentiated and undifferentiated phenotypes, and may possess amoeboid movement. Usually pluri/totipotent, they may express germ‐cell markers, but often lack germ‐line sequestering, and typically do not reside in discrete niches. ASCs may constitute up to 40% of animal cells, and participate in a range of biological phenomena, from whole‐body regeneration, dormancy, and agametic asexual reproduction, to indeterminate growth. They are considered legitimate units of selection. Conceptualizing this divergence, we present an alternative stemness metaphor to the Waddington landscape: the ‘wobbling Penrose’ landscape. Here, totipotent ASCs adopt ascending/descending courses of an ‘Escherian stairwell’, in a lifelong totipotency pathway. ASCs may also travel along lower stemness echelons to reach fully differentiated states. However, from any starting state, cells can change their stemness status, underscoring their dynamic cellular potencies. Thus, vertebrate ASCs may reflect just one metazoan ASC archetype.