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