My Database Professor told us to use:
SELECT A.a1, B.b1 FROM A, B WHERE A.a2 = B.b2;
Rather than:
SELECT A.a1, B.b1 FROM A
Your professor should speak with Gordon Linoff, who is a computer science professor at Columbia University. Gordon, and most SQL enthusiasts on this site, will almost always tell you to use explicit join syntax. The reasons for this are many, including (but not limited to):
FROM and WHERE clauses.Regarding performance, as far as I know, both versions of the query you wrote would be optimized to the same thing under the hood. You can always check the execution plans of both, but I doubt you would see a significant difference very often.