The process in which relatively unspecialized cells acquire specialized structural and/or functional features that characterize the cells of the spinal cord. Differentiation includes the processes involved in commitment of a cell to a specific fate. [ GOC:cls GOC:dgh GOC:dph http://purl.obolibrary.org/obo/go/references/0000021 GOC:jid http://www.ncbi.nlm.nih.gov/pubmed/11262869 ]