A militia is a part-time entity. They are only active full-time when specifically activated, otherwise they go about their day job and train occasionally. It used to be that most militaries were mostly made up of militiamen called up from the lands owned by the heads of each particular army. A few standing armies existed throughout European history but they were the exception rather than the rule.

A government had to pay wages for a standing army all year round. They had to accommodate the soldiers somewhere. They had to feed them. Much easier to call them up when you needed them and dismiss them when you had no more need for them.

In the early US, the militias were militias because they were called up ad hoc from the local populations. They were intended to be for the people so it became quite important that the militias be seen to be drawn from the local area, and to be seen interacting in regular life. Of course, the US didn't exactly have much money as a new country either.

With the increased mechanisation of war it became more complicated to train recruits. It came to a point of sophistication where competency could only be gained if soldiers trained most of the year. At this point, they couldn't hold down their regular lives so that's when militias become militaries.