I have this sql :
SELECT * FROM table WHERE `end` >= '2016-06-20 00:00:00' AND end <= '2016-06-26 00:00:00'
You're comparing full dates & times. and
00:00:00 comes BEFORE
19:00:00, therefore your 19:00:00 value is outside the specified range.
if you want to include all times on a particular date, then compare only the date values, e.g.
WHERE date(end) BETWEEN '2016-06-20' AND '2016-06-26'