What to call a winged unicorn?

What is a word for a winged unicorn or horned pegasus? I've heard a few ways of describing such a fantastical beast, but I don't know which is correct.

They are known as both Alicorns (ali- supposedly from ala (wing), and corn meaning horn), as well as Pegi(a)corn, a portmanteau of Pegasus and Unicorn (I've seen both an i and an a used).

which of these is most 'correct', and did one come first? Furthermore, Wikipedia says that

Alicorn

The horn itself [of the unicorn] and the substance it was made of was called alicorn, and it was believed that the horn holds magical and medicinal properties

So that would make my supposed etymology above wrong.

Solution 1:

Alicorn is the most common word used to describe said beast, however, in the Xanth series, there are also PegaCorns and UniPegs. All three creatures look exactly the same in the series, which is a subtle joke, and the only way to tell them apart is to ask them.