Aircraft registration is unique to each aircraft. Each one begins with country code follow by numbers or characters. However wikipedia says that Taiwan and China both use prefix B. So who actually own the right to use prefix B? If two of them do not co-ordinate the use of prefix them there can be two planes of same registration in the sky. So how things work out here.
From your second link:
Aircraft registered in the People’s Republic of China traditionally have had "B-" followed by four digits.
B-0000 to B-9999
Since 2018, the following registration schemes are also in use:
B-000A to B-999Z (General) B-00A0 to B-99Z9 (General) B-00AA to B-99ZZ (General)
And for Taiwan:
B-00000 to B-99999 after 1990s
so there won't be any confusion, one has 4 digits/characters after the dash, the other 5 digits.