MySQL INNER vs LEFT JOIN different order - php

Question

Why do this two queries return different result set when they have the same ORDER BY.
Only difference in query is that first time I user INNER JOIN an it takes about 5 seconds.
Second time I used LEFT JOIN and it took 0.05 seconds. In both cases they return exactly 43.000 rows, but tck.id order is different and I can't figure out why or in which way?
SELECT tck.*, acc.ac_name
FROM support_tickets tck
INNER JOIN support_ticket_accounts acc USING (id_support_ticket_account)
WHERE tck.id_company = 2 AND tck.st_status = 1 ORDER BY tck.st_priority DESC
Edit:
SELECT tck.*, acc.ac_name
FROM support_tickets tck
LEFT JOIN support_ticket_accounts acc ON tck.id_support_ticket_account = acc.id_support_ticket_account
WHERE tck.id_company = 2 AND tck.st_status = 1
ORDER BY tck.st_priority DESC;
+----+-------------+-------+--------+---------------+------------+---------+-------------------------------+-------+-----------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+--------+---------------+------------+---------+-------------------------------+-------+-----------------------------+
| 1 | SIMPLE | tck | ref | id_company | id_company | 5 | const | 37586 | Using where; Using filesort |
| 1 | SIMPLE | acc | eq_ref | PRIMARY | PRIMARY | 4 | tck.id_support_ticket_account | 1 | |
+----+-------------+-------+--------+---------------+------------+---------+-------------------------------+-------+-----------------------------+
SELECT tck.*, acc.ac_name
FROM support_tickets tck
INNER JOIN support_ticket_accounts acc ON tck.id_support_ticket_account = acc.id_support_ticket_account
WHERE tck.id_company = 2 AND tck.st_status = 1
ORDER BY tck.st_priority DESC;
+----+-------------+-------+------+-------------------------------------+----------------------------+---------+-------------------------------+------+---------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+------+--------------------------------------+---------------------------+---------+-------------------------------+------+---------------------------------+
| 1 | SIMPLE | acc | ALL | PRIMARY | NULL | NULL | NULL | 5 | Using temporary; Using filesort |
| 1 | SIMPLE | tck | ref | id_company,id_support_ticket_account | id_support_ticket_account | 5 | acc.id_support_ticket_account | 2085 | Using where |
+----+-------------+-------+------+--------------------------------------+---------------------------+---------+-------------------------------+------+---------------------------------+

Answer 1

I think using temporary is responsible for the delay (but I don't see why it's necessary for one query and not the other one). I think creating multi-column index should help:
CREATE INDEX filter
ON support_tickets(id_company, st_status, st_priority)
USING BTREE;

Answer 2

If you just ORDER BY tck.st_priority DESC multiple different recordsets are posible and can be returned, for each of both cases (left or inner). That is because you must have a lot of records that has the same st_priority so any of them can came in no particular order
Add more fields to the order by clause to give any record unique possible position and you will have same order on both querys.