Boundary and range description of between in mysql

SELECT * FROM `test` where id BETWEEN 3 and 7;
Equivalent to SELECT * FROM `test` where id>=3 and id<=7;
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SELECT * FROM `test` where id NOT BETWEEN 3 and 7;
Equivalent to SELECT * FROM `test` where id<3 or id>7;

BETWEEN '2018-01-22' AND '2018-01-30'

SELECT * FROM Test a WHERE a.CREATE_DATE BETWEEN '2018-01-22' AND '2018-01-30'   
ORDER BY a.CREATE_DATE desc 

SELECT * FROM TABEL a WHERE a.CREATE_DATE BETWEEN '2018-01-22' AND '2018-01-30'   
ORDER BY a.CREATE_DATE desc
    2018-01-29 23:45:35.0 20180129
    2018-01-29 23:45:33.0 20180129
    2018-01-29 00:10:58.0 20180129
    2018-01-29 00:10:45.0 20180129
    2018-01-28 23:42:23.0 20180128
    2018-01-28 23:39:39.0 20180128
SELECT * FROM TABEL a WHERE a.CREATE_DATE BETWEEN '2018-01-22' AND '2018-01-29'   
ORDER BY a.CREATE_DATE desc
    2018-01-28 23:42:23.0 20180128
    2018-01-28 23:39:39.0 20180128
    2018-01-28 00:13:22.0 20180128
    2018-01-28 00:13:19.0 20180128
    2018-01-27 23:23:02.0 20180127
    2018-01-22 00:09:59.0 20180122
    2018-01-22 00:09:56.0 20180122
    2018-01-22 00:01:53.0 20180122

select * from bips_hpd_helpdesk a WHERE str_to_date(from_unixtime(a.REPORTTIME,'%Y-%m-%d'),'%Y-%m-%d') 
BETWEEN '2018-01-16' AND '2018-01-27' ORDER BY from_unixtime(a.REPORTTIME,'%Y-%m-%d') DESC ;

select * from bips_hpd_helpdesk a WHERE str_to_date(from_unixtime(a.REPORTTIME,'%Y-%m-%d'),'%Y-%m-%d') 
BETWEEN str_to_date('2018-01-16','%Y-%m-%d') AND str_to_date('2018-01-27','%Y-%m-%d')

from_unixtime(a.REPORTTIME,'%Y-%m-%d') AS reportTime,a.REPORTTIME,  
             str_to_date(from_unixtime(a.REPORTTIME,'%Y-%m-%d'),'%Y-%m-%d %h:%i:%s') AS reportTime22
        FROM test a WHERE str_to_date(from_unixtime(a.REPORTTIME,'%Y-%m-%d'),'%Y-%m-%d %h:%i:%s') 
        BETWEEN str_to_date('2018-01-16','%Y-%m-%d %h:%i:%s') AND str_to_date('2018-01-27 %h:%i:%s','%Y-%m-%d')
     #subdate(curdate(),date_format(curdate(),'%w')-1) AND subdate(curdate(),date_format(curdate(),'%w')-8)
        ORDER BY from_unixtime(a.REPORTTIME,'%Y-%m-%d') DESC;