The process in which a relatively unspecialized cell acquires specialized features of a parenchymal cell. Parenchymal cells are the most abundant and versatile cells in plants. They have very few distinguishing characteristics and botanists classify them as any cell type that cannot be assigned to any other structural or functional class. They can redifferentiate and dedifferentiate and are involved in storage, basic metabolism and other processes. The cells are polyhedral, typically with thin, non-lignified cellulose cell walls and nucleate living protoplasm. They vary in size, form, and wall structure.