Nazgul, Ringwraiths relationship

My brother and I are in a heated argument over the relationship between Nazgul and Ringwraiths.

He says the Nazgul are the winged creatures that the Ringwraiths ride.

I say the Nazgul and the Ringwraiths are one in the same (which seems to be supported everywhere I look here on the net).

I think one reason he thinks this is due to this quote from ROTK; Book V; Chap 1, Minas Tirith (page 25 in my book):
"Pippen did not answer. He looked at the grat walls, and the towers and brave banners, and the sun in the high sky, and then at the gathering gloom in the East; and he thought of the long fingers of that Shadow: of the orcs in the woods and the mountains, the treason of Isengard, the birds of evil eye, and the Black Riders even in the lanes of the Shire-and of the winged teror, the Nazgul."

Here is does sort of seem that the Black Riders and the Nazgul are different persons.

I found some other references to the Nazgul to aid me in my argument (Most noteably, ones in FOTR, fefore the winged beasts were mentioned), but they are not necessarily 100% convincing.

I need some proof that the Nazgul and the Ringwraiths are indeed one in the same.

Thanks

<font size=1 color=339966>[ 8:07 PM December 22, 2003: Message edited by: neo_geo ]