The process in which a relatively unspecialized cell acquires specialized features of a sieve cell. A sieve cell is a type of sieve element that has relatively undifferentiated sieve areas (with narrow pores). The sieve areas are rather uniform in structure on all walls; that is, there are no sieve plates. Typical of gymnosperms and lower vascular plants. The sieve element is the cell in the phloem tissue concerned with mainly longitudinal conduction of food materials.