update mysql.user set authentication_string=password('two') where user='root' and host='localhost';

set password for 'root'@'localhost' = password("one");

flush privileges;

^^ You’ll be unable to log in as root/localhost after the above using “one” as the password, but “two” will work.

A preexisting authentication_string should not take priority over the result of SET PASSWORD FOR.

This is a problem for installations that are migrated from MySQL 5.7 because these can still have authentication_string values around.