score:5
Long story short, mainland China (PRC) and Taiwan (ROC) don't recognize each other so they don't want to stamp each others passports / stick visa in there. The pragmatical workaround in place right now is that both nations issue another document to visitors from the other country (i.e. like a visa, but on its own piece of paper in my overly simplified words).
The details are nicely described here for PRC citizens travelling to ROC and here the other way round. The following is a brief and less accurate summary of mine:
Taiwanese can apply for the permit in China Travel Service (CTS) Limited's Hong Kong or Macau branches or through travel agencies in Taiwan.
a document issued by the National Immigration Agency of the Republic of China
Upvote:4
To add to the other answer:
For a mainland/Hong Kong/Macau resident to travel to Taiwan, they will need a "中華民國臺灣地區入出境許可證" ("Exit & Entry Permit for the Taiwan Area of the Republic of China") from the ROC authorities.
For a Taiwan resident to travel to the mainland, they will need a "台湾居民来往大陆通行证" ("Mainland Travel Permit for Taiwan Residents") from the PRC authorities. They will use their ROC passport to enter and exit the ROC side.