The relationship part gets explained a bit in the new update so I won't be spoiling it.
The powered up state. In previous versions, Mr. White would invite you to meet him if you kill 50 humanoids. If you go to the meeting place with Suong in your party, she will have an argument with him revealing that she is not just an ordinary hunter. If you go talk to her afterward, she will say some unique lines and from that point on, she will be using different equipment and be much stronger if you recruit her. That's the powered up state. New version has the dialogue (Altered from previous versions) and she will still be stronger after you meet Mr. White and choose her.