Here's how hardpoint works.
If you're in the hardpoint and get a kill, or kill someone in the Hardpoint, you get +125 for a Hardpoint Kill.
When you capture a Hardpoint, you get +200 for the Hardpoint Capture.
If say there's one enemy in the Hardpoint, and you and one other teammate are in the Hardpoint too, then after that guy on the other team dies, you both get the capture, since you both were in it.
If your teammate leaves the Hardpoint, so noone is in it and your team had it last, then you walk in, you won't get the points since your team captured it last.
If your team takes control of the Hardpoint and then it switches, it's a new Hardpoint so you can capture it and still get the +200.