Setting aggregate result to local variable can change query plan

MariaDB [RHE_MANAGER]> explain SELECT MAX(`CT_ID`) FROM `CONTRATS`;

+------+-------------+-------+------+---------------+------+---------+------+------+------------------------------+

| id   | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra                        |

+------+-------------+-------+------+---------------+------+---------+------+------+------------------------------+

|    1 | SIMPLE      | NULL  | NULL | NULL          | NULL | NULL    | NULL | NULL | Select tables optimized away |

+------+-------------+-------+------+---------------+------+---------+------+------+------------------------------+

1 row in set (0.00 sec)

explain SELECT @max:=MAX(`CT_ID`) FROM `CONTRATS`;

+------+-------------+----------+-------+---------------+--------------+---------+------+---------+-------------+

| id   | select_type | table    | type  | possible_keys | key          | key_len | ref  | rows    | Extra       |

+------+-------------+----------+-------+---------------+--------------+---------+------+---------+-------------+

|    1 | SIMPLE      | CONTRATS | index | NULL          | CT_EXPORTRHI | 2       | NULL | 2679710 | Using index |

+------+-------------+----------+-------+---------------+--------------+---------+------+---------+-------------+