No, the colonial militias were state troops, there being no regional governments. Whatever the founders thought of a regular army, they only managed without one for less than ten years.
Actually you both are correct. They were regional troops within the state. Most militia units were men banded together from the same county, towns, group of towns, etc. That is part of the reason why there is not just one state militia from each state.
For example, men of SW Virginia did not serve in the same units as NE Virginians. (I'm using Virginia as a state, not a specific example). But men from both regions were still part of the Virginia militia.
And another argument when someone mentions that militia meant the U.S. military. Explain to them that the Constitution says the Federal Government must create an Army and Navy. It says nothing about Federal Militias. Hence, the 2nd amend. is not oriented at military personnel because they would be a different entity. or something like that