SQL Server: What is the difference between CROSS JOIN and FULL OUTER JOIN?

Question

A cross join produces a cartesian product between the two tables, returning all possible combinations of all rows. It has no on clause because you're just joining everything to everything.

A full outer join is a combination of a left outer and right outer join. It returns all rows in both tables that match the query's where clause, and in cases where the on condition can't be satisfied for those rows it puts null values in for the unpopulated fields.

This wikipedia article explains the various types of joins with examples of output given a sample set of tables.

One thing that might not always be obvious to some is that a cross join with an empty table (or result set) results in empty table (M x N; hence M x 0 = 0)

A full outer join will always have rows unless both M and N are 0.

I'd like to add one important aspect to other answers, which actually explained this topic to me in the best way:

If 2 joined tables contain M and N rows, then cross join will always produce (M x N) rows, but full outer join will produce from MAX(M,N) to (M + N) rows (depending on how many rows actually match "on" predicate).

EDIT:

From logical query processing perspective, CROSS JOIN does indeed always produce M x N rows. What happens with FULL OUTER JOIN is that both left and right tables are "preserved", as if both LEFT and RIGHT join happened. So rows, not satisfying ON predicate, from both left and right tables are added to the result set.

For SQL Server, CROSS JOIN and FULL OUTER JOIN are different. CROSS JOIN is simply Cartesian Product of two tables, irrespective of any filter criteria or any condition.

FULL OUTER JOIN gives unique result set of LEFT OUTER JOIN and RIGHT OUTER JOIN of two tables. It also needs ON clause to map two columns of tables.

Table 1 contains 10 rows and Table 2 contains 20 rows with 5 rows matching on specific columns.

Then CROSS JOIN will return 10*20=200 rows in result set.

FULL OUTER JOIN will return 25 rows in result set. INNER JOIN will return matching rows, hence, 5 rows in result set.

FULL OUTER JOIN (or any other JOIN) always returns result set with less than or equal to Cartesian Product number.

Number of rows returned by FULL OUTER JOIN equal to (No. of Rows by LEFT OUTER JOIN) + (No. of Rows by RIGHT OUTER JOIN) - (No. of Rows by INNER JOIN).