What is the difference between Postgres DISTINCT vs DISTINCT ON?

DISTINCT and DISTINCT ON have completely different semantics.

First the theory

DISTINCT applies to an entire tuple. Once the result of the query is computed, DISTINCT removes any duplicate tuples from the result.

For example, assume a table R with the following contents:

#table r;
a | b 
---+---
1 | a
2 | b
3 | c
3 | d
2 | e
1 | a

(6 rows)

SELECT distinct * from R will result:

# select distinct * from r;
 a | b 
---+---
 1 | a
 3 | d
 2 | e
 2 | b
 3 | c
(5 rows)

Note that distinct applies to the entire list of projected attributes: thus

select distinct * from R

is semantically equivalent to

select distinct a,b from R

You cannot issue

select a, distinct b From R

DISTINCT must follow SELECT. It applies to the entire tuple, not to an attribute of the result.

DISTINCT ON is a postgresql addition to the language. It is similar, but not identical, to group by.

Its syntax is:

 SELECT DISTINCT ON (attributeList) <rest as any query>

For example:

 SELECT DISTINCT ON (a) * from R

It semantics can be described as follows. Compute the as usual--without the DISTINCT ON (a)---but before the projection of the result, sort the current result and group it according to the attribute list in DISTINCT ON (similar to group by). Now, do the projection using the first tuple in each group and ignore the other tuples.

Example:

select * from r order by a;
     a | b 
    ---+---
     1 | a
     2 | e
     2 | b
     3 | c
     3 | d
    (5 rows)

Then for every different value of a (in this case, 1, 2 and 3), take the first tuple. Which is the same as:

 SELECT DISTINCT on (a) * from r;
  a | b 
 ---+---
 1 | a
 2 | b
 3 | c
 (3 rows)

Some DBMS (most notably sqlite) will allow you to run this query:

 SELECT a,b from R group by a;

And this give you a similar result.

Postgresql will allow this query, if and only if there is a functional dependency from a to b. In other words, this query will be valid if for any instance of the relation R, there is only one unique tuple for every value or a (thus selecting the first tuple is deterministic: there is only one tuple).

For instance, if the primary key of R is a, then a->b and:

SELECT a,b FROM R group by a

is identical to:

  SELECT DISTINCT on (a) a, b from r;

Now, back to your problem:

First query:

SELECT DISTINCT count(dimension1)
FROM data_table;

computes the count of dimension1 (number of tuples in data_table that where dimension1 is not null). This query returns one tuple, which is always unique (hence DISTINCT is redundant).

Query 2:

SELECT count(*)
FROM (SELECT DISTINCT ON (dimension1) dimension1
FROM data_table
GROUP BY dimension1) AS tmp_table;

This is query in a query. Let me rewrite it for clarity:

WITH tmp_table AS (
   SELECT DISTINCT ON (dimension1) 
     dimension1 FROM data_table
     GROUP by dimension1) 
SELECT count(*) from tmp_table

Let us compute first tmp_table. As I mentioned above, let us first ignore the DISTINCT ON and do the rest of the query. This is a group by by dimension1. Hence this part of the query will result in one tuple per different value of dimension1.

Now, the DISTINCT ON. It uses dimension1 again. But dimension1 is unique already (due to the group by). Hence this makes the DISTINCT ON superflouos (it does nothing). The final count is simply a count of all the tuples in the group by.

As you can see, there is an equivalence in the following query (it applies to any relation with an attribute a):

SELECT (DISTINCT ON a) a
FROM R

and

SELECT a FROM R group by a

and

SELECT DISTINCT a FROM R

Warning

Using DISTINCT ON results in a query might be non-deterministic for a given instance of the database. In other words, the query might return different results for the same tables.

One interesting aspect

Distinct ON emulates a bad behaviour of sqlite in a much cleaner way. Assume that R has two attributes a and b:

SELECT a, b FROM R group by a

is an illegal statement in SQL. Yet, it runs on sqlite. It simply takes a random value of b from any of the tuples in the group of same values of a. In Postgresql this statement is illegal. Instead, you must use DISTINCT ON and write:

SELECT DISTINCT ON (a) a,b from R

Corollary

DISTINCT ON is useful in a group by when you want to access a value that is functionally dependent on the group by attributes. In other words, if you know that for every group of attributes they always have the same value of the third attribute, then use DISTINCT ON that group of attributes. Otherwise you would have to make a JOIN to retrieve that third attribute.

The first query gives the number of not null values of dimension1, while the second one returns the number of distinct values of the column. These numbers obviously are not equal if the column contains duplicates or nulls.

The word DISTINCT in

SELECT DISTINCT count(dimension1)
FROM data_table;

makes no sense, as the query returns a single row. Maybe you wanted

SELECT count(DISTINCT dimension1)
FROM data_table;

which returns the number of distinct not null values of dimension1. Note, that it is not the same as

SELECT count(*)
FROM (
    SELECT DISTINCT ON (dimension1) dimension1
    FROM data_table
    -- GROUP BY dimension1 -- redundant
    ) AS tmp_table;

The last query yields the number of all (null or not) distinct values of the column.