Photography, like any art or craft (and which you choose to call it may depend on your personal attitude about the discipline), is a broad subject. Dividing it into categories can make it easier to talk about different approaches to taking pictures, and it can make deciphering the history of photography and photographic concepts simpler.
Because it is such a multi-faceted subject, though, there is no one simple way to categorize the different types of photography. It can be divided up based on subject matter - architectural photography versus portraits, for example. It can be categorized by philosophical approach, the intent, or the concept by which the picture-taking is organized, such as fine art versus commercial photography, or photography for advertising versus photography to bring about social change. Finally, photography can be categorized by the techniques or equipment used to make the images, like HDR photography as opposed to simple single-exposure images, or large format photography rather than 35mm photography.
However it's categorized, though, if you're going to call yourself a photographer - amateur or professional - you'll probably find it useful to familiarize yourself with the many types of photography. This can also be a good way to discover subjects and ways of approaching photography that you might not have thought of otherwise; you might even find your life's passion this way, or expand an existing passion in a new direction.