Sun's revenge doesn't have anything to do with Jay's revenge.
After their respective mother's deaths, both went through grief and guilt. But their backgrounds were so important to understand where that desire came from.
When his mother died in mysterious circumstances, Jay felt responsable because he knew his mother was struggling with her job and he was suspicious about her colleagees. He was too Young to have fully understandment of what was really happening and didn't have any power back then. Still he knew that eventually, he would become owner of everything that was hers. Jay felt powerless and felt the need to blame someone who could do something and that's when he tried to hurt Boss. A little bit for punishment and another bit because he wanted to feel powerful over anything. But Boss won and broke his arm. Instead of gaining resentment towards him, Jay used this experience as a lesson: if you want to honor your mother you will have to become someone powerful.
Now for Sun things went pretty different. He was young and reckless and experiencing love back then. He was feeling great being the one providing money to Bank and also his family. I think he was kind of urging to have his own life. When his mother and brother died, he fell into a spiral of despair. He felt guilty for falling into Bank's spell. Sun, didn't feel powerless, he felt like he wasn't paying attention to everything happening because he was looking at Bank, but that wasn't worthy.
He lost the most important and the only thing he ever really had and his neglicence was actually the real reason why this happened. Understanding that, he assumed his responsability in it. And only lived to pay his debt. He didn't have any other purpose. But then he heard Sunny speaking and that's literally when his own survival instinct found a way to save himself: maybe if he could blame Bank on some of the stuff that happened maybe Sun could use revenge as a purpose to live.
The truth is, Sun's guilt and responsability is real, but at the end of the day he was too young. He can't change what happened but he could build some life from what is broken and will never come back. The desire of revenge was long enough to give him a reason. Then, when he finally understood that Sunny's fault was all an illusion, he had a support system to help him go through that, and reason to fight the depression.
