You are incorrect. There are two categories of intelligence agencies in the US as a matter of law, with significantly different legal authority and structure.
Intelligence agencies like the CIA, FBI, et al are non-military. NSA is explicitly a military agency and operates under military authority. The easiest way to tell the difference is that the Director of military agencies is always an active military flag officer. It isn't just a superficial distinction, they operate quite differently.
Intelligence agencies like the CIA, FBI, et al are non-military. NSA is explicitly a military agency and operates under military authority. The easiest way to tell the difference is that the Director of military agencies is always an active military flag officer. It isn't just a superficial distinction, they operate quite differently.