OK; so, Nikon-Canon dictionary seems to say: Continuous Focus = AI Servo, Single Point = One Shot, D9 = AI Focus.
In that case you'd choose Continuous Focus, in which once the selected focus point zones in, it'll track the target. For subjects that can be told/made to remain static, you'd use Single Point. D9 is like a combination of the two and, like any jack of all trades, it might not work all the time; I never use this mode: it essentially is Single Point but quickly switches to Continuous Focus if it detects the target moving.
What I typed above regarding point extension was in reference to how the Continuous Focus mode works, in which you select a focus point (or a group of them) of the many your viewfinder has and use it to lock on the target, so that you're not using the central point all the time and have to be constantly locking focus and then reframing. Around those points that are marked in the viewfinder, there are other points/sensors that are not visible (they never light up): they're helper points that can aid in retaining focus when tracking a moving subject in Continuous Focus mode. These points can be disabled via an option in one of the menus, as sometimes they might interfere with the tracking (kinda paradoxical, but ah well). At least that's how it is in the Canon system, and it varies also by camera.
What Nikon is this of yours?