Логично. RTFM.

If crypt() is not available on your system, ENCRYPT() always returns NULL.

MD5(string)
Calculates a MD5 checksum for the string. Value is returned as a 32 long hex number that may, for example, be used as a hash key.

mysql> select MD5("testing")
-> 'ae2b1fca515949e5d54fb22b8ed95575'

This is a "RSA Data Security, Inc. MD5 Message-Digest Algorithm".

PASSWORD(str)
Calculates a password string from the plaintext password str. This is the function that is used for encrypting MySQL passwords for storage in the Password column of the user grant table.

mysql> select PASSWORD('badpwd');
-> '7f84554057dd964b'

PASSWORD() encryption is non-reversible. PASSWORD() does not perform password encryption in the same way that Unix passwords are encrypted. You should not assume that if your Unix password and your MySQL password are the same, PASSWORD() will result in the same encrypted value as is stored in the Unix password file. See ENCRYPT().