This question comes up all the time, and most (non-lawyer) people seem to use the terms almost interchangeably. Or, at the very least, they use “copyright infringement” when they mean “trademark infringement.” (The reverse is much rarer.)
Copyrights and trademarks, generally, have nothing to do with each other. It’s possible to infringe a trademark in a copyrighted artwork, and it’s possible to infringe a copyrighted artwork in the creation of a trademark, but either a use (of either) is infringing, or it isn’t. What exactly the use is is not relevant to whether a copyright or a trademark is being infringed. It might be relevant to Fair Use defenses or damages, but not to the question most people are worried about, which is “Can I do this without infringing someone else’s rights in the first place?”
Trademarks are used to identify the source of a good or service. If you buy something with a Mickey Mouse logo on it, what’s really protected is the consumer’s knowledge that that product either comes from Disney, or from a licensee of Disney.
Copyrights are used to protect artistic creation. You can’t draw your own picture of Mickey Mouse and do whatever you want with it, because Mickey Mouse as an artistic creation is copyrighted.
I used Der Maus as an example because he’s a really good one of how the two things can be intertwined. Eventually, theoretically, the copyright on Mickey Mouse will expire, and people will be able to use him as an element in artistic creations. (This is called “entering the public domain.”) However, as long as Disney uses him to identify the source of goods and services, the trademark will endure. (Trademarks don’t expire: they lapse when the seller of the good or service stops using them for a protracted period of time.)
Another really good example is Bram Stoker’s famous creation “Dracula.” Dracula, the novel, is out of copyright. Anybody who wants to can write stories about Dracula. (They can’t infringe on the copyrights of the later movies, though.) However, suppose that the estate had filed a trademark application for “Dracula” brand opera capes. As long as the estate sells (or licenses the mark for sales of) opera capes, nobody else can make Dracula opera capes.
“Aha!” I hear you cry. “What if I get the trademark ‘Dracula’ for publishing books? Then nobody else can publish Dracula books!” Clever! But no. The Trademark Office will not allow the registration of marks which are functional or merely descriptive. I’m allowed to write about Dracula. I need to be able to identify the character of the book. So such a trademark is both functional and descriptive, and would not be allowed.
Sound complicated? It is. That’s why intellectual property lawyers exist. 🙂 But I hope that this brief explanation will help you understand the basic difference between the two and why the fact that there is no trademark doesn’t mean there is no copyright or vice versa.