Modern Photography/Camera body

The camera body contains all necessary components to facilitate the production of an image.

Point-and-shoot Camera

A point-and-shoot camera contains all necessary components to produce an image.

Even a “professional” photographer may use a P&S camera: If you are primarily shooting on film, it is still a good idea to have a compact digital camera with you. If you find a great location, but notice the scene requires different weather, season [regarding vegetation], or light [regarding time of day], you can use this camera to record this idea for a photo without wasting any film (and possibly also time). This is, of course, only feasible if the location can still be revisited at that point in time. While you may also just take a note on a notepad this does not convey as much information as a photo does; you cannot evaluate whether a trip to a particular destination is really worthwhile. A P&S camera does not weigh too much and still gives you more options (especially in comparison to typical cell phone cameras).

Nevertheless, P&S cameras have been primarily superseded by cell phone cameras.

System Camera

A system camera is a system of replaceable compatible camera components. Replaceable or additional components may be:

usually, the lens, but also
the viewfinder,
the screen,
an extra battery pack,
a motor for film transport,
the sensor, or
the back of the body (e. g. for writing data onto the film).

Replacing those components does not require any special skills or tools.

The advantages of system cameras are:

You can adapt the camera to suit best the given situation. You may choose a very bright lens for available-light photography, or mount a motor for film transport when shooting fast sports scenes, without forcing you to have your most expensive lens in your backpack or carrying a bulky motor when it is not needed.

The disadvantages are:

They are more expensive.
You need to think more about choosing adequate equipment.