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

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.

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.