To add on to TheLethalCarrot's answer, it's interesting to note that in the earlier versions of the story the term Nazgûl seemed to be (inconsistently) used to specifically refer to them when in winged form:
But Wizard King takes to air and becomes Nazgûl, rallies host of Morghul, and assails king.
At same time [Sauron] sends Wizard ...
Nazgûl is Black Speech and is translated as Ringwraiths or sometimes Ring-wraiths. Nazg means ring and gûl means wraith/spirit in the broadest of terms.
gûl is a loan from the "Black Speech" and refers to evil and necromantic arts. Cf. Nazgûl (nazg-gûl).
Parma Eldalamberon XVII, "Words, Phrases and Passages in Various Tongues in The Lord of the Rings"...