Actually it's a mix of the two - the new one only counts urban densities, not political boundaries. China has city municipalities which one could loosely call a metro. These municipalities will often contain surrounding towns and cities, inflating Chongqing for example to 35 million people in an area the size of Belgium.
However, as you mention, they can also - absurdly - cut out large chunks of the city, and definitely anything that's been conjoined. For example Shanghai that's merged with Suzhou, or Shenzhen-Dongguan, Changzhou-Wuxi, Guangzhou-Foshan etc, each of whom are considered separate by jurisdiction.
www.newgeography.com
(The same applies to London in a way, whereby the city proper boundaries take in large amounts of empty rural areas, but also cut out large areas of urbanity).
A third spanner in the works is that 'rural' jurisdictions in these areas are often not rural at all, and only in name due to legislative purposes.
For example Huaxi 'village', Hangzhou is classed as rural (despite its factories, tower blocks, million $ villas and supertall)
http://worldkings.org
The rural jurisdiction is basically in place around Chinese cities so that the surrounding farmer's don't all move to the cities en masse. It requires that the people register where they live rurally, and only own land there regardless of where they work or how much they earn. The result absurdly has been that the 'farmers' have brought the city into the countryside - factories, rich sprawl and apartment blocks have instead cropped up in the 'rural' areas around every city for hundreds of miles. Many of the 'farmers' (read: city workers) made rich and hiring out their land to new farmers:
These 'farmers apartments' go on for hundreds of km outside the eastern cities that operate such laws, and the reasoning behind municipality boundaries - it's pretty much Chinese style, high density sprawl:
http://www.skyscrapercity.com/showthread.php?t=244200
http://www.skyscrapercity.com/showthread.php?t=244200
The city also spreads by taking over the only land it's allowed to -rural - but in effect making it urban in all but name. This slowly knits up the nodes until the area becomes built up and reclassified as urban.
These terraforming areas will now be counted:
In short the new measures get rid of municipal inflation that adds separate cities and empty countryside, but includes conjoined cities and high density sprawl.