That is the way I've heard it too.
If you go to the wedding you take a gift. You only take a shower gift if you attend the shower. You can send something with a friend but usually at a shower the only gifts I've seen opened are the ones from the attendees.
The wedding gift can be delivered before the wedding but can be taken to the wedding too.
If you attend both, then I would think a nice wedding gift but just a small shower gift.