Yes and no (but more "no" than yes")
Miao is the official Chinese designation for a bigger Ethnic group- it's one of the 55 official minority groups and it's an official designation, which means that it can be changed by the government and might not reflect the truth.
The Hmong are an ethnic group that is part of the Miao minority.
This means that every Hmong is a Miao but not every Miao is a Hmnog - so there are some Miao (Hmu, Kho) who are not Hmong.
In short: Hmong is a sub-group of MIao