MySQL doesn't offer a distinction between JOIN
and CROSS JOIN
. They are the same.
In both your examples the clause
WHERE t1.a3 = t2.a1
converts any sort of join into an inner join. The standard way of expressing this query is
SELECT t1.a1, t1.a2, t1.a3
FROM t1
JOIN t2 ON t1.a3 = t2.a1