Onward ticket - book together or separate?

Hi, I’m a British citizen living in Japan. I’ll be travelling from Japan (Fukuoka) to Shanghai, and then onward to somewhere like Taiwan or Hong Kong (to be confirmed). Once I’ve decided - do I have to have 1 ticket from Japan to my final destination, with a stopover in Shanghai, or can I book a single ticket to Shanghai and then a single ticket onward to the final destination (so long as I have them both booked before arriving)?

Hope that makes sense. Thanks for your help.