This is not legal advice. I am not a lawyer. I recently sat for a bar exam and will be sitting for another bar exam. I have taken some IP classes in law school, including trademark law. So, I can just provide you with a general understanding of how the two bodies of law work: copyright law and trademark law.
Trademark law and copyright law protect different things.
Trademark law protects the manufacturer of the article on which the trademark is to be applied. The consumer associates the manufacturer's trademark with the source (the manufacturer). It is this vital consumer association which is protected, as this helps protect, in part, the marketability and hence the manufacturer's influx of $$.
Copyright law, on the other hand, protects the author of the copyright (or subsequent owner if the author transfers the copyright to another). Copyright protects the original expression / creativity of the design.
But, these rights work best when owned by one source. If you, as the designer, owner the copyright, the manufacturer would probably wish to purchase from you the copyright to the design. After all, having layers of protection is more desirable than just having a single layer of protection.
In terms of infringement, then, if you own the copyright and a company owns the trademark, a third party infringer that would be sued by the company would only be liable to the company for trademark infringement. Trademark law and copyright law provide for different remedies regarding infringement.
Conceptually, copyright and trademark protection might seem to be very similar, but remember that two different statutes (the Copyright Act of 1976 and the Lanham Act (federal trademark law)) apply, focus on protecting different individuals, etc.
