MySQL Trigger after update only if row has changed

As a workaround, you could use the timestamp (old and new) for checking though, that one is not updated when there are no changes to the row. (Possibly that is the source for confusion? Because that one is also called ‘on update’ but is not executed when no change occurs)
Changes within one second will then not execute that part of the trigger, but in some cases that could be fine (like when you have an application that rejects fast changes anyway.)

For example, rather than

IF NEW.a <> OLD.a or NEW.b <> OLD.b /* etc, all the way to NEW.z <> OLD.z */ 
THEN  
  INSERT INTO bar (a, b) VALUES(NEW.a, NEW.b) ;
END IF

you could use

IF NEW.ts <> OLD.ts 
THEN  
  INSERT INTO bar (a, b) VALUES(NEW.a, NEW.b) ;
END IF

Then you don’t have to change your trigger every time you update the scheme (the issue you mentioned in the question.)

EDIT: Added full example

create table foo (a INT, b INT, ts TIMESTAMP);
create table bar (a INT, b INT);

INSERT INTO foo (a,b) VALUES(1,1);
INSERT INTO foo (a,b) VALUES(2,2);
INSERT INTO foo (a,b) VALUES(3,3);

DELIMITER ///

CREATE TRIGGER ins_sum AFTER UPDATE ON foo
    FOR EACH ROW
    BEGIN
        IF NEW.ts <> OLD.ts THEN  
            INSERT INTO bar (a, b) VALUES(NEW.a, NEW.b);
        END IF;
    END;
///

DELIMITER ;

select * from foo;
+------+------+---------------------+
| a    | b    | ts                  |
+------+------+---------------------+
|    1 |    1 | 2011-06-14 09:29:46 |
|    2 |    2 | 2011-06-14 09:29:46 |
|    3 |    3 | 2011-06-14 09:29:46 |
+------+------+---------------------+
3 rows in set (0.00 sec)

-- UPDATE without change
UPDATE foo SET b = 3 WHERE a = 3;
Query OK, 0 rows affected (0.00 sec)
Rows matched: 1  Changed: 0  Warnings: 0

-- the timestamo didnt change
select * from foo WHERE a = 3;
+------+------+---------------------+
| a    | b    | ts                  |
+------+------+---------------------+
|    3 |    3 | 2011-06-14 09:29:46 |
+------+------+---------------------+
1 rows in set (0.00 sec)

-- the trigger didn't run
select * from bar;
Empty set (0.00 sec)

-- UPDATE with change
UPDATE foo SET b = 4 WHERE a=3;
Query OK, 1 row affected (0.00 sec)
Rows matched: 1  Changed: 1  Warnings: 0

-- the timestamp changed
select * from foo;
+------+------+---------------------+
| a    | b    | ts                  |
+------+------+---------------------+
|    1 |    1 | 2011-06-14 09:29:46 |
|    2 |    2 | 2011-06-14 09:29:46 |
|    3 |    4 | 2011-06-14 09:34:59 |
+------+------+---------------------+
3 rows in set (0.00 sec)

-- and the trigger ran
select * from bar;
+------+------+---------------------+
| a    | b    | ts                  |
+------+------+---------------------+
|    3 |    4 | 2011-06-14 09:34:59 |
+------+------+---------------------+
1 row in set (0.00 sec)

It is working because of mysql’s behavior on handling timestamps.
The time stamp is only updated if a change occured in the updates.

Documentation is here:
https://dev.mysql.com/doc/refman/5.7/en/timestamp-initialization.html

desc foo;
+-------+-----------+------+-----+-------------------+-----------------------------+
| Field | Type      | Null | Key | Default           | Extra                       |
+-------+-----------+------+-----+-------------------+-----------------------------+
| a     | int(11)   | YES  |     | NULL              |                             |
| b     | int(11)   | YES  |     | NULL              |                             |
| ts    | timestamp | NO   |     | CURRENT_TIMESTAMP | on update CURRENT_TIMESTAMP |
+-------+-----------+------+-----+-------------------+-----------------------------+