The concept of identity is used both (i) to distinguish a system as a particular material entity that is conserved as such in a given environment (token-identity: i.e., identity as permanence or endurance over time), and (ii) to relate a system with other members of a set (type-identity: i.e., identity as an equivalence relationship). Biological systems are characterized, in a minimal and universal sense, by a highly complex and dynamic, far-from-equilibrium organization of very diverse molecular components and transformation processes (i.e., 'genetically instructed cellular metabolisms') that maintain themselves in constant interaction with their corresponding environments, including other systems of similar nature. More precisely, all living entities depend on a deeply convoluted organization of molecules and processes (a naturalized von Neumann constructor architecture) that subsumes, in the form of current individuals (autonomous cells), a history of ecological and evolutionary interactions (across cell populations). So one can defend, on those grounds, that living beings have an identity of their own from both approximations: (i) and (ii). These transversal and trans-generational dimensions of biological phenomena, which unfold together with the actual process of biogenesis, must be carefully considered in order to understand the intricacies and metabolic robustness of the first living cells, their underlying uniformity (i.e., their common biochemical core) and the eradication of previous-or alternative-forms of complex natural phenomena. Therefore, a comprehensive approach to the origins of life requires conjugating the actual properties of the developing complex individuals (fusing and dividing protocells, at various stages) with other, population-level features, linked to their collective-evolutionary behavior, under much wider and longer-term parameters. On these lines, we will argue that life, in its most basic sense, here on Earth or anywhere else, demands crossing a high complexity threshold and that the concept of 'interidentity' can help us realize the different aspects involved in the process. The article concludes by pointing out some of the challenges ahead if we are to integrate the corresponding explanatory frameworks, physiological and evolutionary, in the hope that a more general theory of biology is on its way.