Neurogenesis is a lifelong process, generating neurons in the right amount, time and place and with the correct identity to permit the growth, function, plasticity and repair of the nervous system, notably the brain. Neurogenesis originates from neural progenitor cells (NPs), endowed with the capacity to divide, renew to maintain the progenitor population, or commit to engage in the neurogenesis process. In the adult brain, these progenitors are classically called neural stem cells (NSCs). We review here the commonalities and differences between NPs and NSCs, in their cellular and molecular attributes but also in their potential, regulators and lineage, in the embryonic and adult brains. Our comparison is based on the two most studied model systems, namely the telencephalon of the zebrafish and mouse. We also discuss how the population of embryonic NPs gives rise to adult NSCs, and outstanding questions pertaining to this transition.