The early concept of the genus Sinningia was that it contained tuberous plants with campanulate ("slipper") flowers, such as
These flowers were usually white or creamy or lavender or purple. The other tuberous plants had red tubular flowers and were classified in the genus Rechsteineria. This genus included
This seemed like a plausible classification until Carl Clayberg went to work on these plants in the 1950s and 1960s. He crossed (for instance) S. eumorpha with R. cardinalis and not only got hybrids, he got fertile hybrids. Very fertile hybrids.
Although fertility of hybrids between two species has been surpassed by molecular genetics as a measure of the distance between two species, it is still a good indicator. If crossing two species yields very fertile hybrids, they are likely to be quite close. A glance at the crossing chart based on Clayberg's work shows that the DNA studies have confirmed his species associations.
Thus, Sinningia eumorpha and Rechsteineria cardinalis were more closely related to one another than either was to (for instance) Sinningia speciosa or Rechsteineria aggregata. This meant that the Sinningia/Rechsteineria dichotomy didn't work.
Work on floral evolution about the same time made it clear that flower shapes and colors were determined more by adaptations to pollinators than by evolutionary background. Thus, slipper shapes like that of Sinningia eumorpha were the result of selection for bee pollination, while tubular shapes like that of Sinningia cardinalis were the result of selection for hummingbird pollination. Flower shape and color changed more readily under the pressure of natural selection than did (for instance) the number and location of nectaries.
Of the two genus names, Sinningia was the older, and therefore had pushing-and-shoving rights. Rechsteineria, as the kid, got shunted aside. The upshot was that the known Rechsteineria species were gradually transferred to Sinningia, leaving Rechsteineria a more-or-less empty shell.
Another early genus name for some species now in Sinningia is Corytholoma. It is not clear to me what set these species apart, but Perret et al., in their paper on DNA comparisons, used Corytholoma as the name of one of their sinningia subgroups, the one containing S. aggregata and its relatives.
From time to time, it has been suggested that the name Rechsteineria should be resurrected, usually with the intention of using the name for the traditional Rechsteinerias, like R. cardinalis and R. lineata in the Dircaea clade. Unfortunately, that will not work. The type species of Rechsteineria is R. allagophylla, which is in the Corytholoma clade, which isn't the traditional Rechsteineria territory at all -- it includes traditional Sinningia species like S. richii and S. barbata. Expanding Rechsteineria a little to bring in the Sinningia clade would not work either because the Sinningia clade (almost certainly) includes S. helleri, the type species for Sinningia, which has precedence. So there is no way S. cardinalis is ever going to be a Rechsteineria again.