"the militia" is simple. It's what's written in Article 1 Section 8.
The militia is merely an organisation that can be called up into federal service, has officers appointed by the state etc.
It is not just people who choose to get together armed. That would be dangerous and the Supreme Court has ruled this is not the case anyway.
Your militia that is "merely an organization" is the very essence of "people who choose to get together armed."
You have to remember that the militia is there to PROTECT the constitution.
Both from outside invaders and from the government.
In order to do this it needs to be organised.
What the founders didn't want were armed groups of people who would be a threat to the legitimate government and constitution. But they wanted an organised group that could take down an illegitimate government.
The balance is difficult. So they made "the militia" with the states having the power to appoint officers. The states couldn't have armies. But they had their militia, that could be called up to federal service when needed.
All this was designed to be the balance.
Having unorganised militias is not part of this plan. The "unorganised militia" at present is merely a manner to stop people demanding the right to be in the National Guard. The "unorganised militia" doesn't have state appointed leadership, so it can't actually do anything though.