How genetic changes are linked to morphological novelties and developmental constraints remains elusive. Here we investigate genetic apparatuses that distinguish fish fins from tetrapod limbs by analyzing transcriptomes and open chromatin regions (OCRs). Specifically, we compared mouse forelimb buds with the pectoral fin buds of an elasmobranch, the brown-banded bamboo shark (Chiloscyllium punctatum). A transcriptomic comparison with an accurate orthology map revealed both a mass heterochrony and hourglass-shaped conservation of gene expression between fins and limbs. Furthermore, open-chromatin analysis suggested that access to conserved regulatory sequences is transiently increased during mid-stage limb development. During this stage, stage-specific and tissue-specific OCRs were also enriched. Together, early and late stages of fin/limb development are more permissive to mutations than middle stages, which may have contributed to major morphological changes during the fin-to-limb evolution. We hypothesize that the middle stages are constrained by regulatory complexity that results from dynamic and tissue-specific transcriptional controls.