Welll ... they CAN be the same. But that's not how "navigation" is usually used.
"Nautical" is an adjective meaning "related to ships or sailing".
"Navigation" is a noun that most often is used to mean "the science or practice of plotting and following a course for travel". It CAN also mean "traffic of ships".
So for example, one might say, "Bob is an expert at navigation. He can plot a course from any place in the world to any place else." "Navigation" was, I think, originally used to refer to plotting course by ship, but is also used to talk about the course of an airplane or a car.
As to the second meaning, the US Navy regularly talks about "engaging in freedom of navigation exercises", which basically means sailing through contested sections of the ocean to make a point that they're allowed to be there. That is, they're basically using "navigation" to simply mean "travel by ship". Maybe this usage is common among sailors, but I don't hear it much in common speech.
People sometimes use "navigation" metaphorically to mean finding one's away around anything. Like, "Let me explain how to navigate this software's menus."
"Navy" is not the same as "nautical". "Navy" is a noun meaning a branch of a nation's military devoted to fighting at sea. "Navy" is a noun while "nautical" is an adjective, and "nautical" can refer to both military and civilian use of boats and ships, while "Navy" only refers to military. Well, like almost any word, it can be used in a non-literal way. Like you might say, "Wow, Bob just bought a fourth boat! The man has his own navy!"