There are DSLR's, point and shoot cameras (also known as compact cameras), mirrorless cameras, medium format, etc.
You can find a list of different cameras at digital photography school's website
What Kinds Of Cameras Are There?
There are lots of different kinds of cameras. First, there are film cameras for still photographs and movies. These cameras range from simple point and shoot cameras to very sophisticated 35mm or 4x5 cameras. Movie cameras can also be different sizes also, such as 8mm, 16mm, 35mm and 70 mm. ≈There are digital cameras for both still images and video. There are also special purpose cameras for things we can't see such as infrared, or very high speed cameras for capturing fast events, as well as the very large format Imax camera.