Correct. HK and Macau have their own immigration policies, and Taiwanese cannot reside in those places unless they are sponsored by an employer (or family members, etc.).
There is a special residence ID for Taiwanese living in China (shown in the photo tango posted above), which is basically the same as the National ID issued to Chinese citizens. It follows the same numbering format, and basically makes living and working in China much easier.
This is different from the Taibaozheng travel document (shown in the photo Satellite posted above) issued to Taiwanese travelers to China.