I've noticed that AF-C can pulse and flutter quite a bit, even when the subject is moving very slowly. Shots taken during a pulse will definitely be out of focus.
You know, at one point I feel confused. So let's get the difference between AF-C and AF-S sorted.
While on AF-C, The focus would continually search and reposition? or its only continually searching when I'm actually focusing by half pressing or back button focus?
In AF-C, it is continually trying to focus as long as you are giving it a command to do so. That means a half press of the shutter release, or pressing the BBF programmed button. In the default mode from the factory, the camera will always fire a shot when you press the shutter release in AF-C. It doesn't check for a properly focussed image. It simply shoots. This can be changed in your setup.
While on AF-S holding the back button focus would focus once and until I don't lift my finger and press again it wont focus again. Correct?
In AF-S, the camera will attempt to focus, then stop when it thinks it is focused (or just can't focus and times out). Hold the button, release the button, it doesn't matter. It maintains that focus setting, regardless of movement of the subject or the camera. After obtaining focus, if the subject or camera moves, you'll get out of focus shots. When you again press the button, it will focus once again. Then maintain that new setting. Wash, rinse, repeat. At any given time, shoot as many pictures you want. They will all be at that fixed focus distance. Good or bad. The camera can be setup to not fire a shot if it doesn't think it is focussed. There are multiple settings for this with interactions between those settings. It can be a bit difficult to understand those interactions.