Sooo nazgul are the ones flying on the dragon things and ringwraiths are the ones on horses? Or is nagul just the name of the dragon things?

1) "Nazgûl
Sauron's Nine Servants

A word from the Black Speech, usually translated 'Ringwraith'; the name of the nine Men corrupted by the power of Sauron's Nine Rings, and transformed into his dark and deathless servants."
Source and further information:
http://www.glyphweb.com/arda/n/nazgul.html


2) "Black Riders
The Nazgûl on horseback
One of the forms taken by the Nazgûl when they went abroad in Middle-earth; black-cowled figures riding coal-black horses.

In the closing years of the Third Age, the Black Riders were sent by their master Sauron into the northern lands to seek for the land of 'Shire', where he had learned the Ring could be found. They rode up the Greenway, and their leader, the Lord of the Nazgûl, established himself in the gorge of Andrath, south of Bree. Meanwhile, the Riders discovered the Shire, but too late to capture the Ring-bearer. They gave chase to Frodo and his companions eastward to Rivendell, and close enough to wound him on one occasion. However, their ambitions were foiled by Aragorn and Glorfindel, and they were ultimately overcome by the powers of Elrond and Gandalf.

After the loss of their horses, the Black Riders made their way back to Minas Morgul and acquired new mounts: vast flying beasts that carried them far above the lands of Middle-earth."
Source and further information:
http://www.glyphweb.com/arda/b/blackriders.html

Read the books. This is not a sarcastic comment, they are very good.

Nazgul, black riders and ringwraiths are all just different names for the kings of men who were taken by the power of the ring. The dragon they fly on is called a fell beast.