Actually, psychopaths and sociopaths are considered variations of Anti Social Personality Disorder instead of two separate diagnoses, they're colloquial terms at best. Though this is what's popularly understood :
Psychopaths tend to be colder and calculative, devoid of feelings like empathy or guilt and favor long term benefits.
Sociopaths tend to be more impulsive, doing things at the spur of the moment, using their traits to manipulate others at the expense of their wellbeing, they may feel empathy or guilt but it is rarely their top priority.
For me, I think subin's just very insecure and lonely, peer pressure gets to her and she feels the need to act a certain way so people find her unique. Especially since people have already labeled her as the "quirky" one, she feels the need to keep up with it, till she met someone actually unusual, putting her already established reputation at risk. So she acts up out of fear of losing her "crazy" title to Sarang.
Again, sociopathy/psychopathy are rarely used as a diagnoses anymore, more specific clinical terms like ASPD are used to describe these cases.
And, no need to be so harsh on yourself, you are pretty smart for making this observation, and looking for insight. Please give yourself credit for taking the initiative to learn, we learn new things everyday! Have a good day/night :)
I gave it some thought again and I think Subin might be narcissistic instead. Which checks out with the deep insecurity and constant need for attention. Kept wondering why she was reminding me of someone I knew, well it's because that person was narcissitic. She might be a textbook Narcissist. While Sarang is a Psychopath. Sounds like the dark triad in a way, would it make the the council president Machiavellian?

why does someone want to seem crazy or 'psychopathic' Infront of people, I don't think Subin a psycho but more like a sociopath
But idk, I just did one lil google search on what was the difference between a sociopath and a psychopath and sociopath seemed to be more like Subin
(Please call me retarded if you think I'm wrong)