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 MyDramaList)

They are both romance stories that include time travel.
The Plot of the stories are very similar.
I enjoyed the dramas a lot and found them very intriguing.