Fabio is actually not right, if hours, minutes and seconds will be included this
where date >= '2013-06-01' and date <= '2013-06-06'
becomes internally
where date >= '2013-06-01 00:00:00' and date <= '2013-06-06 00:00:00'
So you actually just select 1 second of 2013-06-06, not the whole day!
Same with BETWEEN of course. To get the whole day of 2013-06-06 you'd have to write
where date >= '2013-06-01' and date <= '2013-06-06 23:59:59'
or
where date BETWEEN '2013-06-01' AND '2013-06-06 23:59:59'
Go ahead, try it yourself (or see it live in an sqlfiddle):
create table foo (my_date date, my_timestamp timestamp, my_datetime datetime);
insert into foo values ('2013-06-06', '2013-06-06 12:23:34', '2013-06-06 13:35:48');
select * from foo
where
my_date <= '2013-06-06'; /*returns row*/
select * from foo
where
my_timestamp <= '2013-06-06'; /*does NOT return row*/
select * from foo
where
my_datetime <= '2013-06-06'; /*does NOT return row*/
select * from foo
where
my_timestamp <= '2013-06-06 23:59:59'; /*returns row*/
select * from foo
where
my_datetime <= '2013-06-06 23:59:59'; /*returns row*/