PostgreSQL supports the same 4 basic types of SQL JOINS as MySQL:

INNER JOIN
LEFT JOIN
RIGHT JOIN
FULL OUTER JOIN (same as FULL JOIN)

The key difference is that PostgreSQL uses the term FULL OUTER JOIN instead of just CROSS JOIN.
Other than the terminology difference for the cross join, PostgreSQL and MySQL support the same core JOIN types, and they work the same way - combining rows from two tables based on a JOIN condition (typically a equality match on some common column(s)).
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