Flora of North America recognizes a broader view of Xanthisma and a more restricted view of Machaeranthera. This view is well supported by molecular data. The details can be read here.
FNA isn't alone in this viewpoint with ITIS, Calflora, SEINet, BONAP and Ajo Peak to Tinajas Altas: A flora of Southwestern Arizona all using Xanthisma.
The Plant List includes both names as accepted, but this doesn't really make sense because both represent the same species, it is just a question of which genus is used. The Macharanthera name takes pinnatifida and the Xanthisma name takes spinulosum.
Note also this paper for a recently published article for information regarding the species in the context of what was the broader Machaeranthera.