Using PostgreSQL what is the difference between a smallint and a bool for storing boolean?
Always store boolean data as boolean. Only exotic exception imaginable.
Just to address the storage angle in addition to what you posted as answer:
boolean requires 1 byte on disk, smallint requires 2. But that's not the whole story.
smallint (like other integer types and unlike boolean) also has special needs for alignment padding. It can only start at an even offset from the start of the tuple data. So another byte is consumed every odd time (literally).
In a worst case scenario, when mixing with types that require 8-byte alignment like bigint or timestamp / timestamptz:
SELECT pg_column_size(row(&quot;char&quot; 'a', FALSE   )) AS char_bool
     , pg_column_size(row(&quot;char&quot; 'a', int2 '1')) AS char_int2
     , pg_column_size(row(text 'abcdef', TRUE    , now())) AS text7_bool_ts
     , pg_column_size(row(text 'abcdef', int2 '1', now())) AS text7_int2_ts;  -- worst case

 char_bool | char_int2 | text7_bool_ts | text7_int2_ts
-----------+-----------+---------------+---------------
        26 |        28 |            40 |            48

Details:

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