That`s actually not a stupid question at all. Instead, it brings out the
stupidity of modern corporate "jargon," and how it completely confuses
any sort of reasonable communication. A corporate "partner" is just
that, modern junk-slang.
I suppose the original intent was that two related businesses would
mutually support one another`s efforts. So AT&T provides
telecommunications capabilities, where Yahoo! provides Web
organization, structure, and site hosting.
The SBC (now ATT) and Yahoo! "partnership" meant that neither company
had to invest all that money in what the other already could provide.
To my way of seeing it, I think this type of "partnering" is a way to
combine resources without a leveraged buyout, merger, or acquisition of
the other company.
Of course at an enterprise level, it leads to some interesting problems
when some outside company buys one of the partnering companies. :-) But
at your level, I think it makes the most sense to think of it as you`ve
said, a mutual exchange of resources to provide a better overall
service to your similar customers.