Os documentos do MySQL que você mencionou disseram "use qualquer um deles". Mas o seguinte
FLUSH LOGS supports optional modifiers to enable selective flushing of individual logs (for example, FLUSH BINARY LOGS).
A log-flushing operation does the following:
If general query logging or slow query logging to a log file is enabled, the server closes and reopens the general query log file or slow query log file.
If binary logging is enabled, the server closes the current binary log file and opens a new log file with the next sequence number.
If the server was started with the --log-error option to cause the error log to be written to a file, the server closes and reopens the log file.
não funciona no Windows para arquivos abertos (consulte Como posso renomear arquivos e pastas no Windows que estão em uso? , Renomeando um arquivo aberto ).
Além disso, os documentos dizem
SET GLOBAL general_log = 'OFF'; ...
This method works on any platform