SQL Join - MySQL/PostgreSQL difference?

Greetings.

I'm working with a product provided by a third part that interfaces to
data housed in a database of your choice. Previously, my choice was
MySQL - apparently it handled certain queries too slowly, so I'm giving
PostgreSQL a shot. Here's the query:

SELECT
a.Number,
a.Code,
a.Text
FROM
b,
a
WHERE
(b.Id = a.Id) AND
(VersionId = 'key1') AND
(Category = 'key2') AND
(b.d_Id = 'key3')
ORDER BY
a.Number;

(my apologies: I had to 'mangle' the table/column names because of NDA)

So my question is this: would this query operate differently in MySQL
than in PostgreSQL? The reason I ask is that this query in MySQL
returns results, yet in PostgreSQL it does not. I read a post about
PostgreSQL not supporting outer joins, but I don't have enough
experience with SQL to determine if this is such a query or not. Please
advise.

Any help will be (as always) sincerely appreciated.

--
Brice Ruth
WebProjkt, Inc.
VP, Director of Internet Technology
http://www.webprojkt.com/