NYC is not 13,318 sq mi which is what your talking about aka an area ~200 miles wide and bigger than the state of Maryland. By comparison DC is 61 square miles total your figure is like lumping DC, Baltimore, and Richmond VA into one metro area.

https://en.wikipedia.org/wiki/New_York_metropolitan_area

DC and Baltimore are typically lumped in as one metro area.

https://en.wikipedia.org/wiki/Baltimore%E2%80%93Washington_m...

Not really: "It is composed primarily of two major metropolitan statistical areas, the Washington–Arlington–Alexandria, DC–VA–MD–WV MSA and the Baltimore-Columbia-Towson, MD MSA. In addition, six other smaller urban areas not contiguous to the main urban area but having strong commuting ties with the main area are also included in the metropolitan area."

I mean some people talk about the Northeast megalopolis. https://en.wikipedia.org/wiki/Northeast_megalopolis Boston, New York City, Philadelphia, Baltimore, Washington DC, and some times Richmond. But, that does not mean Boston and DC are somehow the same city.

>"The "NYC" urban area encompasses NYC + Westchester + Long Island + Newark + parts of CT."

Not it does not, that is the "Tri-State" area. I have never heard anyone use the term "NYC Urban area." What you are saying makes it sounds as if those places are suburbs of New York City and none of them are. New York City is 5 boroughs.

Also I think you are confusing Manhattan and New York City. Half the daily population of Manhattan are commuters:

http://cityroom.blogs.nytimes.com/2013/06/03/commuters-nearl...

Okay but then you can't compare that to Stockholm proper. It should be exceedingly obvious to anyone who has even Google image searched the two cities that NYC is much denser.

I didn't compare it to Stockholm proper. I compared the NYC urban area (basically, NYC and it's suburbs and satellite cities) to Stockholm's urban area. Stockholm proper is less dense than NYC proper, but that is by itself not that useful a number. More people live outside NYC in the urban area as live inside NYC. The opposite is true for Stockholm.