Insulin-producing β cells created from human pluripotent stem cells have potential as a therapy for insulin-dependent diabetes, but human pluripotent stem cell-derived islets (SC-islets) still differ from their in vivo counterparts. To better understand the state of cell types within SC-islets and identify lineage specification deficiencies, we used single-nucleus multi-omic sequencing to analyse chromatin accessibility and transcriptional profiles of SC-islets and primary human islets. Here we provide an analysis that enabled the derivation of gene lists and activity for identifying each SC-islet cell type compared with primary islets. Within SC-islets, we found that the difference between β cells and awry enterochromaffin-like cells is a gradient of cell states rather than a stark difference in identity. Furthermore, transplantation of SC-islets in vivo improved cellular identities overtime, while long-term in vitro culture did not. Collectively, our results highlight the importance of chromatin and transcriptional landscapes during islet cell specification and maturation.