Enzo, I understand your confusion.
The U.S. Army "belongs to" the Federal government, and is commanded by the President. "National Guards" are like militias--they are armed forces within individual states of the US that are trained and equipped like the U.S. Army, and wear the same uniforms. But they are normally commanded by the Governors of individual states, and used for state and local emergencies. They represent a long tradition of "citizen armies"--private citizens who are part-time soldiers, who train and drill on weekends and during summers--but who can be called to action when needed. Usually, a Governor will "call out" (activate) the National Guard during emergencies such as floods, hurricanes, riots, etc. National Guards are not the Governors' "private armies"--they are more like a state and local military resource.

However, the President of the US can activate National Guard units with the consent of states' governors. US law says the following about how the President can federalize the National Guard:


Whenever—
(1) the United States, or any of the Territories, Commonwealths, or possessions, is invaded or is in danger of invasion by a foreign nation;
(2) there is a rebellion or danger of a rebellion against the authority of the Government of the United States; or
(3) the President is unable with the regular forces to execute the laws of the United States;
the President may call into Federal service members and units of the National Guard of any State in such numbers as he considers necessary to repel the invasion, suppress the rebellion, or execute those laws. Orders for these purposes shall be issued through the governors of the States [emphasis added] or, in the case of the District of Columbia, through the commanding general of the National Guard of the District of Columbia.

(I copied this from a Cornell University site.)

One of America's greatest strengths is our system of "checks and balances" between federal, state and local power. The provision of US law that requires the President of the US to get Governors' approval before federalizing various National Guards is one of the most important "checks and balances." Permitting the President to federalize the national guard removes one of those safeguards and can lead to abuses of power.