The purpose of a copyright is to protect works of authorship as fixed in a tangible form of expression (i.e. a thing not an idea). The art, photos, writing and design you make fall under this category. It protects people from copying or redistributing your work.
The purpose of a trademark is to protect words, phrases and logos used in federally regulated commerce to identify the source of goods and/or services. It represents an enterprise or a business. It protects your company from other companies trying to look like you. In the case your your logo, it would be used to prevent others from using a confusingly similar mark or name.
It is common for certain types of expression (like a brand) to sit under both copyright and trademark. If you are trying to protect a title, slogan, or other short word phrase, generally you want a trademark as a copyright does not cover such types of expression alone.
If your design is intended to identify the source of goods or services (i.e. a logo), it should be trademarked.
While copyright registration is primarily an administrative process (you fill out a form and send it off), trademark registration is an adversarial process.
It includes a substantive review of potentially conflicting marks in order to prove your uniqueness within a market segment.
For example: say you are doing a trademark search for a local motorcycle tuner/builder called "Redwing Motorcycle Company". During the trademark vetting process you would probably get an argument from Redwing Shoes saying the name/mark is too close to theirs (Redwing does sell a series of Motorcycle boots, so they may have some grounds here even though they are in a very different market). You might also get a call from Honda saying "We are a large motorcycle manufacturer. We have a famous product line called the 'GoldWing'. Our corporate color is Red." You will have to fight it out.
Other companies will be aggressive in protecting themselves. US trademark law works under a "use it or lose it" principle. Read up on how Carol Shelby lost the rights to his famous Cobra car design. So many people copied it (without him going after them) that it was ruled that he no longer owned it.
So, understand that if you do seek a trademark, you need to be willing and able to protect it.
The key thing to understand is that Copyright and Trademarks are proven and protected in very different ways. Copyrights are low-hanging fruit and should absolutely be done. Trademarks are a longer, more expensive process and you want a good Trademark lawyer to guide you through the process.
