Clarification: The camera battery refers to a portable source to bring electric power to a camera. A digital camera cannot be operated without the battery.
There are two kinds of batteries which can be used in digital camera. A proprietary battery refers to one unit which is suitable for one or some digital camera models. The shapes of these batteries are often rectangular or square and you can recharge them.
An alkaline battery refers to a popular kind of the camera battery which is often manufactured in mass. You often throw this kind of battery away after using it, for example, cylindrical AAA or AA batteries. You can find many various uses of these batteries for consumer electronics devices.
Commonly, a digital camera only can work with one kind of battery.