why do Chinese, hong kong and taiwanese have different passports?

Lo Wu Control Point (Chinese: 羅湖管制站) is a Hong Kong immigration control point in Lo Wu, New Territories. It sits within the Frontier Closed Area that runs along the border with mainland China. Its counterpart across the border is the Luohu Port in Shenzhen, China.

why is north korea and south korea a different countries? 

 of course they have border patrol that's what passports are for