mysql> CREATE TABLE testtab (
    ->   label VARCHAR(30) PRIMARY KEY,
    ->   a VARCHAR(10),
    ->   b VARCHAR(10)
    -> );
Query OK, 0 rows affected (0.09 sec)
 
mysql> INSERT INTO testtab VALUES('both null',NULL,NULL);
Query OK, 1 row affected (0.03 sec)
 
mysql> INSERT INTO testtab VALUES('a null',NULL,'b not null');
Query OK, 1 row affected (0.04 sec)
 
mysql> INSERT INTO testtab VALUES('b empty string','a','');
Query OK, 1 row affected (0.03 sec)
 
mysql> INSERT INTO testtab VALUES('a null, b empty string',NULL,'');
Query OK, 1 row affected (0.04 sec)
 
mysql> INSERT INTO testtab VALUES('equal non-empty strings','x','x');
Query OK, 1 row affected (0.03 sec)
 
mysql> INSERT INTO testtab VALUES('non-equal non-empty strings','x','y');
Query OK, 1 row affected (0.04 sec)
 
mysql> SELECT * FROM testtab;
+-----------------------------+------+------------+
| label                       | a    | b          |
+-----------------------------+------+------------+
| a null                      | NULL | b not null |
| a null, b empty string      | NULL |            |
| b empty string              | a    |            |
| both null                   | NULL | NULL       |
| equal non-empty strings     | x    | x          |
| non-equal non-empty strings | x    | y          |
+-----------------------------+------+------------+
6 rows in set (0.04 sec)
 
mysql> SELECT * FROM testtab WHERE a=b;
+-------------------------+------+------+
| label                   | a    | b    |
+-------------------------+------+------+
| equal non-empty strings | x    | x    |
+-------------------------+------+------+
1 row in set (0.04 sec)
 
mysql> SELECT * FROM testtab WHERE a<>b;
+-----------------------------+------+------+
| label                       | a    | b    |
+-----------------------------+------+------+
| b empty string              | a    |      |
| non-equal non-empty strings | x    | y    |
+-----------------------------+------+------+
2 rows in set (0.03 sec)
 
mysql> SELECT * FROM testtab WHERE b IS NULL;
+-----------+------+------+
| label     | a    | b    |
+-----------+------+------+
| both null | NULL | NULL |
+-----------+------+------+
1 row in set (0.12 sec)
 
mysql> SELECT * FROM testtab WHERE b IS NOT NULL;
+-----------------------------+------+------------+
| label                       | a    | b          |
+-----------------------------+------+------------+
| a null                      | NULL | b not null |
| a null, b empty string      | NULL |            |
| b empty string              | a    |            |
| equal non-empty strings     | x    | x          |
| non-equal non-empty strings | x    | y          |
+-----------------------------+------+------------+
5 rows in set (0.00 sec)