Militia is Militia, as is referred to in the Constitution several times.
>To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
>To provide and maintain a Navy;
>To make Rules for the Government and Regulation of the land and naval Forces;
>To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
>To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
Army, Navy and Militia are separated purposely to leave states with the power of militia. The 1903 act states what defines militia, and Heller v. District of Columbia established that firearms are, in fact, a right of citizens.
Well that begs the question: who, as stated by the 2nd Amendment, is allowed the right to bear arms? Citizens in the form of a militia. Thus, since citizens are allowed to bear arms, citizens are also allowed to form militias.
Interestingly enough, this also may imply that any such formed militia has to obey orders from the President, or at the very least some structure of state, if they were to wish to remain "legal".