This is a great question. As a licensing artist who has been fighting the Orphan Works Legislation I can answer it for you and give you a heads-up on how things are shifting.
For the Gap the designs are either licensed from the artist who gets a royalty for each item sold or a flat fee for the lot, or the Gap will use an in-house artist and they will own the copyright by default. Both licensing artists and companies register their copyrights with the Library of Congress as an added precaution against image theft.
What I think you are asking about in this question is “Implied Copyright” which was established at the Berne Convention for the Protection of Literary and Artistic Works. This dates back to the late 1800’s and has been adopted by nearly every nation, including the US, who joined in the 1970’s or 80’s. (I would have to look it up to remember exactly when but it is not all that important.)
What the Berne Convention established was that once an artist or author created a work that there was an “implied copyright” to the creator and that punitive damages could be leveled against those who use the work without permission.
There are two problems with relying on “implied consent” for protection. The first is that it is much harder to prove that you own the work in a court of law if you are infringed upon. It comes down to a “he said -she said” sort of deal.
The second issue is that Google and other companies that collect massive amounts of images and literary works have been lobbying to overturn the Berne Convention and allow any work found to be deemed “orphaned” if the creator cannot easily be located. Any work deemed as “orphaned” will be considered royalty-free and can be used without payment to the artist. Additionally- and more devastating- is that the Orphan works ELIMINATES the potential reward the creator can sue for if infringed upon so greatly that it would cost the creator more in legal fees then they could ever hope to recover.
While Orphan Works has not passed yet, it is still being re-written and pushed through and came within hours of passing 18 months ago.
My point in telling you this history, current and past, is to let you know that if you have great designs COPYRIGHT them as a collection in the Library of Congress. It is well worth the trouble and can even be done digitally on line.
Having that piece of paper is the best protection you can have for your work.
Also WATERMARK any images online clearly with your name and copyright. Even if you use small images there is software out there that can increase it to print quality. (I have one of these programs and can assure you it works great.)
Good luck with your venture!
Oh and Trademark is a whole other deal. Logos and stuff have to be legally trademarked.