Equidae
Equidae (sometimes known as the horse family) is the taxonomic family of horses and related animals, including the extant horses, donkeys, and zebras, and many other species known only from fossils. All extant species are in the genus "Equus". Equidae belongs to the order Perissodactyla, which includes the extant tapirs and rhinoceros, and several extinct families.
Equisetaceae
All living horsetails are placed in the genus "Equisetum". But there are some fossil species that are not assignable to the modern genus. "Equisetites" is a "wastebin taxon" uniting all sorts of large horsetails from the Mesozoic; it is almost certainly paraphyletic and would probably warrant being subsumed in "Equisetum". But while some of the species placed there are likely to be ancestral to the modern horsetails, there have been reports of secondary growth in other "Equisetites", and these probably represent a distinct and now-extinct horsetail lineage. "Equicalastrobus" is the name given to fossil horsetail strobili, which probably mostly or completely belong to the (sterile) plants placed in "Equisetites".