Unicorns Etc

The cover of one edition of Poul and Karen Anderson's The Unicorn Trade (see previous post) shows not a horned horse but a small winged horse. CS Lewis' Narnia has unicorns, winged horses, centaurs and other mythological quadrupeds. So how are these quadrupeds related and is a winged horse a "hippogriff"?

According to Wikipedia:

a wyvern has a dragon's head and a reptilian body with two or even no legs (so is not a quadruped);
a gryphon has the head, claws and wings of an eagle but the body, hind legs and tail of a lion;
a hippogriff is like a gryphon but with a horse's instead of a lion's body because it is a cross between a gryphon and a horse.

However, in Neil Gaiman's The Sandman, Morpheus' Castle is guarded by a wyvern, a gryphon and a hippogriff and the third of these is drawn like a winged horse.

The Unicorn Trade includes a short story by Karen Anderson about sphinxes, that I have not read yet. This is not the first time that I have found an interesting parallel between the works of Anderson and Gaiman, although The Unicorn Trade derives its title from a two page poem by Karen Anderson that opens the book.