72 or 144 visa free transit

No, the countries that serve as your immediate points before and after your Chinese destination can be any country of this world including three Chinese territories: Hong Kong, Taiwan and Macau.

The only thing that matters, beside your citizenship (53 eligible countries/citizenship), is that your immediate points before and after your Chinese destination have to be in two different countries (or eligible territories).

You can fly:

Turkey (Istanbul) - Beijing - US (Los Angeles)
US (New York) - Shanghai - Hong Kong
Mongolia (Ulaanbaatar) - Beijing - South Korea (Seoul)

I hope this has cleared all doubts about this scheme. The same rules are valid for both 72 and 144 hour visa free transit, but 72 hours is used in just several smaller Chinese cities. 144 hours scheme is more dominant.