We use transposon-based clonal analysis to identify the lineage classes that make the adult zebrafish caudal fin. We identify nine distinct lineage classes, including epidermis, melanocyte/xanthophore, iridophore, intraray glia, lateral line, osteoblast, dermal fibroblast, vascular endothelium, and resident blood. These lineage classes argue for distinct progenitors, or organ founding stem cells (FSCs), for each lineage, which retain fate restriction throughout growth of the fin. Thus, distinct FSCs exist for the four neuroectoderm lineages, and dermal fibroblasts are not progenitors for fin ray osteoblasts; however, artery and vein cells derive from a shared lineage in the fin. Transdifferentiation of cells or lineages in the regeneration blastema is often postulated. However, our studies of single progenitors or FSCs reveal no transfating or transdifferentiation between these lineages in the regenerating fin. This result shows that, the same as in growth, lineages retain fate restriction when passed through the regeneration blastema.