Barnardia was previously included in Scilla and is a member of the Hyacinthaceae (or the expanded Asparagaceae) family. It consists of two species which flower in autumn before the leaves have developed. Bracts and bracteoles (smaller, secondary bracts) are present.
Barnardia japonica (Thunb.) Schult. & Schult.f., syn. Scilla japonica, syn. Scilla scilloides, is dormant in the summer and then produces linear leaves followed by small starry pink or blue flowers in the fall. According to Plants of the World Online it has three accepted varieties: Barnardia japonica var. japonica with a range of China to temperate Eastern Asia, Barnardia japonica var. litoralis (Konta) M.N.Tamura native to Japan, and Barnardia japonica var. major (Uyeki & Tokui) M.N.Tamura, also native to Japan. This site list 29 taxa as synonyms. This species is unusual as it has two flushes of leaves, one in the spring and another in the fall. Photos 1 and 2 by John Lonsdale, photos 3 and 4 of seed by Rimmer de Vries (the ruler is marked in cm).
The first two photos show plants grown from seed that was identified as Scilla scilloides and the other photos including one of the stalk are photos of plants grown from seed labeled Barnardia numidica. All of these plants in the photos from Mary Sue Ittner are probably Barnardia japonica.
Barnardia numidica (Poir.) Speta is from North Africa (Algeria, the Balearic Islands , Libya, Tunisia). Although seed identified as this species circulates, Jane McGary in several posts to the PBS lists understands that this species is rare and probably not in cultivation and most of this seed is instead seed of one of the varieties of Barnardia japonica. Ali, Syed Shujait; Yu, Yan; Pfosser, Martin & Wetschnig, Wolfgang Wetschnig (2012) in "Inferences of biogeographical histories within subfamily Hyacinthoideae using S-DIVA and Bayesian binary MCMC analysis implemented in RASP (Reconstruct Ancestral State in Phylogenies)", Annals of Botany, 109 (1): 95–107 found here write: "However, it is now believed that B. numidica is not related to Barnardia (data not shown) and should be transferred to a genus of its own." Photos of this species can be found on iNaturalist. The seeds look very different from the seeds of what many of us have grown as Barnardia numidica. The flowers are similar, but also different.
Barnardia scilloides Lindl. syn. Scilla scilloides (sometimes incorrectly called Scilla chinensis) is not accepted by all as some believe this species should be sunk into Barnardia japonica (syn. Scilla japonica.) See above.