WHERE (created BETWEEN '2017-08-01 00:00:00' AND '2017-08-31 23:59:59') AND change_date >= '2017-09-01 00:00:00'
тут вообще никакие функции не нужны.... WHERE
(created BETWEEN UNIX_TIMESTAMP('2017-08-01 00:00:00') AND UNIX_TIMESTAMP('2017-08-31 23:59:59'))
AND
change_date >= UNIX_TIMESTAMP('2017-09-01 00:00:00')
... WHERE (created BETWEEN '2017-08-01' AND '2017-08-31') AND change_date >= '2017-09-01'
... WHERE (created BETWEEN 1501538400 AND 1504216799) AND change_date >= 1504216800
DATE(created) BETWEEN '2017-08-01' AND '2017-08-31'
created BETWEEN '2017-08-01 00:00:00' AND '2017-08-31 23:59:59'