Forward: This is as best as I understand things, but I am by no means a lawyer. Also only applies to the US.
You see the image above. It is both registered with the US Copyright office and available for non-commercial use using Creative Commons.
There is a lot of confusion as to the nature of the two, and many think that the two are independent of each other. That, however, is not true. Copyright is the foundation upon which creative commons is based.
(1) You own the copyright to your images even if you do not register them (unless you transferred it or were working full-time for someone while taking them) with the copyright office. Registering images provides extra legal protection if someone uses your images without your permission. Even more so if you register the images before they are published. It’s a nice legal stick to have. A great resource is: http://asmp.org/content/
(2) Creative Commons is a means of giving the general public a basic license to use your photos in a number of scenarios of your choosing. It was designed to prevent the photographer from having to write a license (or approve the use) of each photo if someone wants to use it in a school report, blog post, etc. There are several different types, so if you are interested find one that fits your comfort level. Some allow people to modify your images. Some don’t. Some allow your images to be used for commercial purposes, etc. All require attribution. Take a look at the different types here: http://creativecommons.
I’m in the camp of not caring if someone uses one of my photos for non-commercial means. For that reason. I try and mark my images as CC on Flickr and 500px. If the photo ends up in a school report that’s great. If it ends up on a personal blog with ads, that’s not.
That’s because I am also in the camp of caring if someone uses one of my photos for commercial means. For that reason I’ve registered virtually my entire photography “collection.” The only ones I skip are personal family photos. Everything else gets registered. Outtakes, double takes, even photos with camera shake. This all happens before any image is posted online (According to the copyright office, posting a picture online is considered “publishing” and adds another layer to the legal web). This process creates a bottleneck in my photo taking to online posting workflow, but guarantees images don’t slip through the cracks. It’s this bottleneck that prevents new groups of images from being published for several months. Even with the bottleneck I feel it’s worth it because registration is a stick I want to have if it’s ever needed.
There is a lot more to this issue that this post doesn’t cover. Such as how many to register at one time, costs, etc. To find out more check here: http://thecopyrightzone.com/
Those guys also have a book, videos, interviews, etc. All of which is worth your time.