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I'll have a go....Single point AF is ideal for stationary subjects. e.g. a bird sitting, you can place the AF point on the eye of the bird when composing your shot. The others can be used for moving subjects and it depends what lens you use and how big your target is relative to the frame. So for example, if you used a long telephoto lens on a teleconverter to shoot a preening bird, you might choose 9 point AF and it will target the spot you select but will AF from any of the 9 points around it. The bird is moving but not a lot, so its movements are within your 9 point AF area. If the bird were a bit more erratic to follow, you might widen the AF area to 21 points. If you were shooting at a shorter distance with a moving subject that fills a lot of the frame, then you might choose 51 point AF. You also have 3D tracking which you can use when the subject is moving erratically. And the AUTO area AF mode will focus on faces, suitable for candid people shots.
AF-S focuses once when you half depress shutter. AF-C continuously focuses. With the latter you use more battery power, which could be one downside. You might use AF-C if your portrait subject were fidgety (children, pets). And in other scenarios AF-C would be a nightmare, e.g. focusing on a wildlife subject amongst foliage moving in the wind, the camera could grab focus on the foliage instead of the subject as the wind moved it in and out of your focus area.
Hope that helps...