只能说我菜，在网上找了下没发现谁解释过他们四个的区别，那就只能自己来了。下面是通过mysql客户端查看到的帮助信息，直接贴解释吧。
user：Returns the current MySQL username and hostname as a string in the utf8 character set.
system_user：SYSTEM_USER() is a synonym for USER().
session_user：SESSION_USER() is a synonym for USER().
current_user：
Returns the username and hostname combination for the MySQL account
that the server used to authenticate the current client. This account
determines your access privileges. As of MySQL 5.0.10, within a stored
routine that is defined with the SQL SECURITY DEFINER characteristic,
CURRENT_USER() returns the creator of the routine. The return value is
a string in the utf8 character set.
The value of CURRENT_USER() can differ from the value of USER().
其实想翻一下再放出来的，怎奈自己那见不人的英语水平，就不翻译了。总的来说：user()、system_user()、session_user()，这三是同一个东西（synonym ）。然后current_user()跟前三个也很像，不过他偶尔又会有点区别。