What is single auto focus and full time auto focus?

I was just messing with camera setting (nikon s5200) and found these two options. First tell me what is the difference b/w them? And then tell me which should be used and when should be used!
and also tell me the meaning of these two option in video mode, will it autofocus during video shoot?

Single auto focus is fixed focus, full time auto-focus (continuous) is meant for everything else, especially when zooming, or it will blur out.

AF-S or Single auto-focus focuses once. If you hold down the shutter release to half pressure the camera will focus once, usually on what is in the middle of the frame - then when you move the camera it will remain focused on that first item that it focused on. You can then re-compose and take the picture. Your subject will still be in focus, but not necessarily in the middle of the picture. Alternatively you could use a different focus point.

AF-C or Continuous or Full time Auto-Focus keeps the camera focusing as long as you have half pressure on the shutter release. If you were trying to follow a moving car or a bird in flight you could keep full time auto-focus on so that the camera would try to keep the subject in focus while you are moving the camera or while the subject is still moving.

As a general rule you will probably use full time AF for moving subjects and fixed AF the rest of the time.

There's sometimes an AF-A auto setting which tries to detect movement and set the correct one for you, but there's no guarantee that the camera will get it right or that the camera will achieve the effect that you want, so it's best to get used to setting it yourself.

Single auto focus is NOT fixed focus. Single auto focus is when you focus on one subject that is not moving. You would use this when taking portraits, like of your friend that is just standing there. The same for video.

Autofocus Full time means the camera continuously focuses. You would use this on a moving subject. Yes, it will autofocus during video recording, but the sound of the lens moving will be picked up by the audio. See page 99 of your manual.

The weekend I'm shooting a horse show.

I use the AF-C setting on the camera an keep the focusing point on top of the subject as it moves through the scene. This assures that the subject remains in focus each time I press the shutter release.

All you have to do is place the focusing point in the part of the frame where your subject will be as you shoot shot after shot while the subject moves around the arena.

It's a real pity that Nikon didn't think to enclose an Instruction booklet with the camera!

Single focus is good for subjects that are not moving. You focus once and shoot. Continuous autofocus is for subjects that are moving, you focus on the subject and keep following it. As you track the subject, the camera keeps focusing on it until you press the button.