difference between the two command, any idea?


GRANT ALL PRIVILEGES ON *.* TO 'oxigen'@'localhost.localdomain' IDENTIFIED BY 'oxigen' WITH GRANT OPTION;

GRANT ALL PRIVILEGES ON *.* TO 'oxigen'@'localhost'
IDENTIFIED BY 'oxigen' WITH GRANT OPTION;

in effect nothing
localdomain would be to identify a windows domain (not absolutlely certain), whereas local host is always the computer the MySQL server is running on. (assuming you have defined localhost in your hosts file)

you can also specify the host using an IP address or IP range eg '192.168.*'