NC is a "Free City" in terms of it's status within the structure of NUSA. Essentially, a territory they claim is theirs, but which they don't actually have the means to exercise control over. So it just functions more or less autonomously.
But it essentially functions as a Japanese Treaty Port in terms of military influence and is the point where East Asian and NUSA criminal and corporate organizations use to bring goods cheaply into and out of the NUSA market with both international and domestic corporations using Night City as a corporate tax haven and tariff-free port of entry. Smuggling is king as everyone seeks to skim their share off the goods as they move inland, each government agency or smuggler serving as competing "taxes" for entry into markets.
NUSA has largely reunited in 2070, but NC is still one of the last holdouts, backed as it is with all the might of Arasaka and the threat of igniting a new Corporate War if NUSA were to try to annex it and actually attempt to assert influence over the city.
The place you noticed the map is a customs checkpoint for leaving the NUSA and entering the city-state of Night City. The whole premise of that opening mission is that you're smuggling contraband over the border.
NC is a stand-alone city-state, kind of like Athens in ancient times or like modern day Singapore. As for the map, I'll let someone else more versed in the lore address that.