The process in which neuroblasts acquire specialized structural and/or functional features that characterize the mature cerebellar stellate cell. Differentiation includes the processes involved in commitment of a neuroblast to a cerebellar stellate cell fate. A cerebellar stellate cell is an inhibitory GABAergic interneuron found in the cerebellar cortex. [ GOC:dgh GOC:dph GOC:cls http://www.ncbi.nlm.nih.gov/pubmed/15157725 GOC:jid http://purl.obolibrary.org/obo/go/references/0000021 ]