The NG is _a_ militia.
The NG is actually two entities in one. Members are simultaneously part of the Reserve components of the US armed forces and a member of the state militia. As such they answer both to the president as members of the armed forces and to the governor as part of the militia. The feds can at any time say "they're federal forces" and take them away from the governor. This is what allows the NG to be shipped overseas. The federal government does not have an enumerated power to use the militia outside the US--only to repel invasion and suppress insurrection. So when the feds want to use them to invade Canada, they say they're part of the US armed forces and place them under US federal command.
There are other militias. For example, many states such as Texas have a State Guard. This is a militia, but they are _not_ enrolled in the US Reserves. States can define other militias.