Using PostgreSQL what is the difference between a smallint and a bool for storing boolean?

First, the size of a smallint is two bytes which is twice the size of a bool:

SELECT
  pg_column_size(1::bool) AS "bool"
  , pg_column_size(1::smallint) AS "si";

 bool | si 
------+-----
    1 |   2

Let's create a small table with 1000 rows and check it out:

CREATE TABLE foo AS
  SELECT
    CASE WHEN x>0.5 THEN 1::smallint ELSE 0::smallint END AS si,
    CASE when x>0.5 THEN true ELSE false END AS b
  FROM ( SELECT random() AS x FROM generate_series(1,1e3) ) AS t;

CREATE INDEX si ON foo (si);
CREATE INDEX b ON foo (b);

Now we can see the table with 40kB:

test=# \dt+ foo
            List of relations
 Schema | Name | Type  | Size 
--------+------+-------+-------
 public | foo  | table | 40 kB

Both indexes are the same size (40kB). And all self-joins (returning 500050 rows in my case) using a seq scan and index scan (with SET enable_seqscan=off) complete in the same amount of time:

EXPLAIN ANALYZE SELECT * FROM foo JOIN foo AS f2 USING (b);
EXPLAIN ANALYZE SELECT * FROM foo JOIN foo AS f2 USING (si);

So really the benefits are that:

• the col size is one byte smaller
• the table shows bool, rather than smallint which is more descriptive
• eliminates room for error if you store 3.
• it's likely to work in third party libraries a bit better.
• it permits slightly more terse SQL, WHERE isEmpty rather than WHERE empty = 1