Crocus sativus belongs to the Iridaceae family. The plant grows from a corm and flowers in autumn. Each blossom carries three red stigmas. Those stigmas are separated from the flower and carefully dried; the finished dried stigma is the saffron used by chefs.
Cultivated saffron is sterile and is propagated vegetatively by dividing corms rather than by ordinary seed production. This helps explain why geography, soil, climate, drying method and local handling traditions create meaningful differences in aroma, appearance and strength even though the culinary spice comes from the same species.
Chef's distinction: when the market speaks about saffron “varieties,” many names actually refer to origin, commercial grade, stigma cut or processing tradition, not to completely different culinary species.