Hi, first post in here, I am Hmong French.
"Hmong" is the romanized term of the word that the Hmong people use to call themselves in their dialect. "Miao" is a mandarin word use to call a minority group where the Hmong are include in. The Miao people have 3 majors sub-group related to the 3 major dialects of this people. They can identify themselves in a different term link to their dialect. For exemple, as a Miao, I call myself "Hmong" in my dialect and my girlfriend (who is Miao too) call her "Hmu" in her dialect. English call me "french" but i call myself "français".
Because majority of the Miao who migrate to the western world are Hmong, this word is use to identify them and not "Miao". Furthermore,the word Miao is confused with a pejorative term "Meo" used by the south east asian people to call them, so it's difficult to them to accept being labelled as Miao.
There is a lot of educated hmong people in the western world but their history were mostly wrongly teached and only vocaly by elder who come from Laos, so most of them lack of knowledge about their history related in China.
China history is really badly know out of China, this is really difficult to learn about chineses minorities history... But Hmong folks believe that when they die, their spirit return to their motherland and they all know that this is in the heart of the Middle Kingdom. Today, with the web and the opening of China, some like me want to know more about our roots and return in China to visit and learn.
Hmong people, as Miao people, are certainly one of the oldest relative of the chinese people.