The Best camera for Sports Action Photography is a D-SLR. The Nikon D90 with a 300mm zoom lens will take spectacular shots and can record video at 24p, but is well over the $800 budget. Very few D-SLR cameras have video capability. There are a lot to choose from that will be good for sports photography such as the Canon XS, Nikon D60 and Sony a300 to name a few. These would be great starter cameras, work well for sports and priced right to still allow you to add the 300mm lens for shooting from the stands.

The Digital uses a Sensor to basically scan a image delivered by the lens into digital components and stores this image on a removable media. The sensor is usually a CMOS (Complementary Metal Oxide Semiconductor) or CCD (Charge-Coupled Device) and sets in the same area as the Film in a traditional camera. The sensor on compact and advanced digital cameras are about the size of a Dime. Sensors on a D-SLR come in twos sizes. Slightly larger than a nickel and the full size sensor (35mm film size).
Compact cameras have a LCD Screen that is used in place of a view finder (eyepiece) to compose the shot. This does not give a good representation of the final image. SLR (Single Lens Reflex) cameras allow the photographer to “See Through the Lens” via Eyepiece to compose a better shot. The image comes though the lens (TTL) and it reflected by a pentaprism or penta-mirror to the eyepiece. When the Shutter release button is pushed the Reflex Mirror (or Prism) flip out of the way and allows the image to be exposed to the sensor (or film).

All camera with a built in flash will automatically enable when in auto mode. Some models with a Pop-Up flash will either pop-up or give you an indication that the flash needs to be opened.

Both are good cameras and will give you good photos. The difference is the D-SLR will grow with you as you grow as a photographer. An Advanced camera will not. Also the Sensor on a D-SLR is larger and that will give you better clarity, color and light sensitivity. Evan thow the Coolpix P80 is a 10.1 megapixel and the D40 is a 6.1, the image will be noticeably better on the D40. Battery life will be longer on a D-SLR. You have Changeable lenses vs a fixed lens on an Advanced. No Shutter lag time and faster burst mode on a D-SLR. As far as ease of use...ALL D-SLR cameras have a FULL Auto mode that make them a Point-and Shoot.
True that Advanced Cameras have a “Movie Mode”...but consider that this mode is designed for e-mail quality video and may be seldom used.