Eva

The story of hero So Si Min, who once ruled the nation with her top-tier hapkido skills as a high school athlete. Seven years later, after becoming a part-time teacher, So Si Min finds herself the target of the evil student Han Soo Kang.
(Source: Soompi)

It follows the life of student Yun Ga Min, who wants to be good at studying but is only good at fighting, as he forms a study group at the worst school on earth and tells a fierce story about college entrance exams. Yun Ga Min looks like a model student but is a student at Yusung Technical High School, which is one of the worst schools to study at. Although he studies extremely hard, his grades don’t rise in the slightest. Despite all that, Yun Ga Min sits diligently at his desk with the goal of going to college. However, when his study group friends get bullied, Yun Ga Min takes off his glasses and school uniform jacket to put his fighting skills to use. Lee Han Gyeong, Yun Ga Min's teacher, dreams of seeing the school change for the better. Lee Han Gyeong tutored Yun Ga Min during her university days and reunites with him when she is appointed as a temporary teacher, holding a secret. (Source: Soompi)

Subsequently, Kim Ji Yong begins living two entirely different lives. On weekdays, he's a model student at the police university. During the weekends, he punishes criminals who'd received light sentences and continue to commit criminal acts. Now called Vigilante, Ji Yong receives help from admirer Cho Kang Ok. Meanwhile, Detective Cho Heon chases after the man called Vigilante. (Source: AsianWiki; edited by kisskh)

Kim Ji Yong begins living two entirely different lives. On weekdays, he's a model student at the police university. During the weekends, he punishes criminals who'd received light sentences and continue to commit criminal acts. Now called Vigilante, Ji Yong receives help from admirer Cho Kang Ok. Meanwhile, Detective Cho Heon chases after the man called Vigilante.

(Source: AsianWiki; edited by kisskh)

They are both romance stories that include time travel.
The Plot of the stories are very similar.

Han Jun Hee's boyfriend Koo Yeon Jun died one year ago. She still hasn't gotten over his death and misses him a lot. One day, she somehow travels back in time to the year 1998 and finds herself as high school student Kwon Min Joo. There, she meets high school student Nam Si Heon. She is surprised to see how much Nam Si Heon resembles her late boyfriend Koo Yeon Jun. (Source: AsianWiki; edited by kisskh)