I don't know squat about either, but this might help clear up the confusion.
30 Encyclopędia Britannica articles, from the full 32 volume encyclopedia
> hornbeam
any of about 25 species of hardy, slow-growing ornamental and timber trees constituting the genus Carpinus of the birch family (Betulaceae), distributed throughout the Northern Hemisphere. The hop-hornbeam (q.v.) is in a different genus of the birch family. A hornbeam has smooth, grayish bark, a short, fluted trunk, and horizontally spreading branches. It differs from ...
> hop-hornbeam
any of about seven species of ornamental trees constituting the genus Ostrya of the birch family (Betulaceae), native to Eurasia and North America. A hop-hornbeam has shaggy, scaling bark and thin, translucent, green leaves with hairy leafstalks. The hoplike, green fruits are composed of many bladderlike scales, each bearing a small, flat nut.
Justin