Visa free entry Guangzhou

As Belgian residents we will be travelling to New Zealand in December. We fly from Paris (France) to Christchurch (New Zealand) and back with a stopover in Guangzhou (China).

The flights Paris-Guangzhou and Guangzhou-Christchurch are booked on a single ticket (luggage checked through) with arrival in Guangzhou around 6 am and departure on the same day in the evening around 23 pm. We also have a day-time hotel stay outside the airport to catch some sleep. (= approximately 17 hours in China)

The return flights Christchurch-Guangzhou and Guangzhou-Paris are booked as two separate tickets (luggage picked up and checked in again) with arrival in Guangzhou on December 27 (6 am) and departure on December 30 (1 am). In that way we'll have 3 days to visit the cities of Guangzhou and Shenzhen. (= approximately 67 hours in China)

Is it correct that on both trips specified above (each time leaving the airport in Guangzhou), we don't need a Chinese Visa, but instead we can apply for the visa free entry (24/144 hours)?