There are essentially three types of cameras that can be used for underwater photography - point-and-shoot, full-featured, and dSLR (digital single-lens reflex camera).
Point-and-shoot is the simplest and most compact type of underwater camera. These cameras are very easy to use and designed for casual, fun pictures or videos. A camera on your smartphone, for example, falls into this category. With the release of underwater housings, many smartphone models can now be used for taking pictures underwater.
Full-featured cameras bridge the gap between point-and-shoot and dSLRs. They combine ease of use and more advanced functionality, which makes them very popular among snorkelers and vacationers. Many waterproof cameras fall into this category.
dSLRs – Digital SLR (Single Lens Reflex) cameras are for those who are serious about photography. Some of the benefits of these cameras include a variety of high-quality interchangeable lenses, better sensors, and no shutter lag. Keep in mind though, that not all dSLRs are supported with underwater housings, so before selecting the camera, make sure there is a housing available for it.