The process in which cells that are products of meiosis acquire the specialized features of ascospores. Ascospores are generally found in clusters of four or eight spores within a single mother cell, the ascus, and are characteristic of the ascomycete fungi (phylum Ascomycota). [source:
GOC:di, GOC:mah, GOC:mcc, PMID:16339736]
Note that ascospores and asci are separate biological structures. The ascus is the structure that contain the ascospores, but the development of the ascus is a different process than the formation of the ascospores themselves; for instance, some mutations affect sporulation without affecting ascus development. For this reason, GO:0030437 ascospore formation and GO:0075317 ascus development are different terms and are not linked.