Going to Plant Database,
type in Sedum,
Click here to view all plants in the genus: Sedum. [At this point IMO there should be something to indicate that there are two names.]
The list comes up in some kind of random order, some say Sedum, some say Stonecrop, some have the Hylotelephium name, some have Rosularia, Prometheum, Phedimus, (and yes, I am the one who would like the entire world to be in strict alphabetical order - probably beating a dead horse with that one), but I cannot see the pattern in the list.
Also, since (I admit I am an idiot) I don't know the difference between 'searching' and 'browsing' I cannot understand why the lists is ordered differently for each.
