The hepthalites & huns

Great,

Basically, the Hephthalites were originally known as the Hua.  The Hua were a nomadic people of northwest China who were similar to the earlier Hsiung-Nu.  Throughout the 5th Century, they succeeded to the Hun heritage of the steppes in a campaign through central Eurasia, from the Tian Shan to the Carpathians.  They ended up in Bactria before eventually establishing themselves in northwest India in the early 600's.  The name "Hephthalite" comes from one of their ruling families.  They were called "Huna" by the Indians and Roman writer Procopius referred to them as the "White Huns."  

We can't really say that they were exactly the same people as Attila's Huns (indications are they were not), but we know for sure that the people of the time knew them as Huns.  It seems that the term "Hun" referred to steppe nomads in general rather than a specific ethnic group.

The southern or "Red" Kidarite vassals to the Kushans in NWFP, became better known as Red Huns from 360 AD after Kidara II led a Bactrian portion of Hunni to overthrow the Kushans in India. At this time Kidarite Hunni (Kidarites) successfully controlled the length of the Oxus from the Hindu Kush all the way to the Aral Sea.

Kidara's southern Xionites were the first "Hunas" to bother India. Indian records note that the Hūna had established themselves in Afghanistan and NWFP in present day Pakistan by the first half of the fifth century, and the Gupta emperor Skandagupta had repelled a Hūna invasion in 455.