It is the both.
The problem with Ile de France cover also rural area.
See the map less than 40% of Ile de France is urbanised
Some part of Ile de France are not in Paris metro and some place outside Ile de France are in Paris metro area.
For me Greater Paris should be the core of urban area (The zone with a hig density, offices, shop..) and not the low density suburbs.
* Paris with 6.7 million inhabitants has a bigger GDP than Greater London and would be one of richiest cities in the world
with Tokyo (8 million) New York (8 million) Greater London (7.5 million) Paris (6.7 million)