Despite from 2 different companies, they can share the same library since the command and registers protocol is the same.
- DS3231 has internal thermal compensated crystal which makes it more precise
- The https://detail.tmall.com/item.htm?id=520058075274&toSite=main Module with DS3231 also contains an AT24C32 I2C eeprom
- Important:
Do not buy TINY RTC module , it has design flaws
See : http://forum.arduino.cc/index.php?topic=177297.0