How to execute UNION without sorting? (SQL)

I notice this question gets quite a lot of views so I'll first address a question you didn't ask!

Regarding the title. To achieve a "Sql Union All with “distinct”" then simply replace UNION ALL with UNION. This has the effect of removing duplicates.

For your specific question, given the clarification "The first query should have "priority", so duplicates should be removed from bottom" you can use

SELECT col1,
       col2,
       MIN(grp) AS source_group
FROM   (SELECT 1 AS grp,
               col1,
               col2
        FROM   t1
        UNION ALL
        SELECT 2 AS grp,
               col1,
               col2
        FROM   t2) AS t
GROUP  BY col1,
          col2
ORDER  BY MIN(grp),
          col1  

"UNION also sort the final output" - only as an implementation artifact. It is by no means guaranteed to perform the sort, and if you need a particular sort order, you should specify it with an ORDER BY clause. Otherwise, the output order is whatever is most convenient for the server to provide.

As such, your request for a function that performs a UNION ALL but that removes duplicates is easy - it's called UNION.

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From your clarification, you also appear to believe that a UNION ALL will return all of the results from the first query before the results of the subsequent queries. This is also not guaranteed. Again, the only way to achieve a particular order is to specify it using an ORDER BY clause.