Just for the record, and in light of finding myself in print with some incorrect information which I didn’t actually write, I offer the following clarification.
The true autumn flowering crocus is in fact a crocus. There are many different species in the genus of crocus, some flowering in spring and some in autumn. Generally, crocus flower around the same time their foliage appears. We don’t have a species name on this pretty autumn crocus in our garden. Trace the botany of crocus back and they are part of the subfamily of Crocoideae, the family of Iridaceae and the order of Asparagales.
Colchicum autumnale flower about the same time for us, but the flowers appear a long time before the foliage so they are sometimes called naked ladies. Equally, they are sometimes referred to as autumn crocus but they are not. Again it is a big genus with many different species but they come from the family of Colchicaceae and the order of Liliales.
Sternbergia are sometimes referred to as autumn crocus but they are no more autumn crocus than colchicums. In fact they are more closely related to narcissi than crocus (a fact I discovered from the Pacific Bulb Society) and they are closely related to amaryllis. However, they flower with their foliage and their blooms, generally yellow, resemble a crocus in form. We have sternbergia in the garden here but they don’t flower overly well for us, possibly because they are essentially a Mediterranean plant which likes a hot, dry summer.
Also widely referred to as naked ladies are Amaryllis belladonna or the belladonna lilies that are mostly seen as roadside plants here. The genus is amaryllis, the species is belladonna (and there is only one other species in that genus) but the sub family (Amaryllidoideae) and then family (Amaryllidaceae) are the same as sternbergia. Trace them back another step on the Linnaeus chart and you find they are from the order of Asparagales which is where they meet the family tree of crocus – quite a long way back, botanically.
The bottom line is that the true autumn crocus is indeed a crocus, though it may be one of many different species.