The urban area is what people refer to as Paris. A good comparison is Los Angeles. Lots of people say they “live in LA” but in fact live in Santa Monica or Long Beach or Pasadena or any of a million other suburbs that together form the Los Angeles urban area.

When people say they live in Paris, 99% of the time they’re not talking about the arbitrary municipal boundaries; they’re talking about the urban area.

When people say they live in LA, 99% of the time they’re talking about the urban area.

When people say they live in Buenos Aires, 99% of the time they’re talking about the urban area.

When people say they live in Tokyo, 99% of the time they’re talking about the urban area.

“Urban area” is simply a term meant to capture what people mean when they refer to a city, unrestricted by the arbitrariness of municipal boundaries.