Note that depending on which flora you consult, both genera may be lumped into one or the other genera. The following is a very short list of barberry species (to be updated later as time permits):
Oregon Grapes: The Genus Berberis
Creeping Barberry, Creeping Oregon Grape: Berberis repens (Synonyms: Berberis amplectens, Berberis aquifolium var. repens, Berberis pumila, Berberis sonnei, Mahonia amplectens, Mahonia pumila, Mahonia repens, Mahonia sonnei, Odostemon pumilus, Odostemon repens)
Barberries and Mahonias: The Genus Mahonia
Fremont's Mahonia: Mahonia fremontii (Synonyms: Berberis fremontii, Berberis higginsiae, Mahonia higginsiae, Odostemon fremontii)
Red Barberry, Algerita, Red Oregon-grape, Mexican Barberry: Mahonia haematocarpa (Synonym: Berberis haematocarpa)