Buddha nature (佛性) was a common synonym of Tathagata garbha (如來藏), so I think the author took the “easy way out” and provided the translation of the more common term. The two expressions refer to the same thing, which is the potential tathagata that resides in ordinary beings.
Garbha is tough to translate - it could mean a fetus, embryo, an inner sanctum of a temple, the inner rooms of an apartment - the basic idea is something hidden inside. Chinese 藏 had the same general meaning. It didn’t have the specifically reproductive meanings, but it could mean internal organs. It was often used for places where valuables are hidden away - a storehouse, granary, treasury, chest, basket, etc. So, it was a common way of translating garbha.