Comparing dates

My date setting is ISO with US conventions, and output from a select
is in the form yyyy-mm-dd (2002-01-18, for example.

When I do a select such as

SELECT * FROM table WHERE date BETWEEN '2001-12-28' AND '2002-01-28'

It misses the entry with date '2002-01-28' (which does exist!).

Likewise,

SELECT * FROM table WHERE date = '2001-12-28' ;

gives me '0 rows'.

The only way I've been able to handle this, so far, is
in this fashion:

SELECT * FROM table WHERE
date BETWEEN 20011228 - .001 AND 20020128 + .001 ;

and similarly instead of = using, I can use

date BETWEEN 20020128 - .001 AND 20020128 + .001

I must be missing something, but I can't find it.

What is the 'right' way to select for a date type = a particular
date, and for BETWEEN to work as advertised?

I have a copy of 'Practical Postgresql', but I can't find the
answer there, or in the online manual. Of course there are a
lot of places to look and I may have missed it.

Thanks,

John Velman