So in any series or film, it is a fundamental rule and understood 
that time travel is a LOOP, and everything is connected.


In 2023, Han Jun Hee is mourning the "supposed" death of a boyfriend whose body is not found in a plane crash. Later she discovered a photo of her look alike girl Kwon Min Ju and her missing boyfriend look alike Nam Si Heon along with an unknown person Jung In Kyu. 

She found out that Kwon Min Ju died in 1998 from her Uncle who tells her that KMJ claimed that she was Han Jun Hee but no one believed her. 

HJH receives a parcel of 1988 Samsung MyMy Stereo mixtape recorder along with a cassette of Seo Jiwon songs. These two objects are a main source of time travel. 

After discovering some facts and still clueless about what is going on she listens to the tape and fell asleep going back in time. HJH wakes up in KMJ body who had an accident after discovering that her mother has fled with her little brother, but it turns out KMJ was attacked by a possible killer and not accident as she claimed to be.

HJH who is in KMJ body quickly handles the situation as she was aware of possible time travel after listening to KMJ Uncle from future. She meets Nam Si Heon who is look alike of Koo Yeon Jun her deceased boyfriendfrom future and a person Jung In Kyu who is NSH best friend.

[...the story takes place in past before HJH is back in future and she further chases her boyfriend whereabouts and finds out more about time travel and KMJ from her Uncle...and she travels back in past to put everything back in its place...]

HJH/KMJ, NSH and JIK, together they struggled in a love triangle and a murder mystery and HJH trying to find the killer and return to future. 

[...Skipping all the story details...]

Still in past, She finds out that NSH is actually KYJ of future after discovering KMJ photo in his bedroom, that she once inquired about it from KYJ of future. Before she ask anything from NSH, she is woken by her friend in future. She runs to KMJ Uncle and ask that he knew everything and that KYJ she loved was actually NSH from past. 

HJH finally discovers that she failed to save KMJ and JIK is arrested for KMJ murder and NSH leaves for America. In 2002, NSH comes back to Korea to meet JIk in prison but he refuses to see him, on his way to hotel, NSH listens to very tape and the bus gets into a violent accident and he is travelled to 2007 as KYJ while NSH dies in accident in past. NSH who is now KYJ in 2007 visits the Uncle and they put together everything together. Since then NSH starts living as KYJ and only Uncle knows that he is NSH and not KYJ. 

Later KYJ meets HJH in a university and he becomes her boyfriend and later when is vanished in plane crash the HJH discovers tha photo and enters into a loop of time. 

Conclusion: 

So it was HJH who was already there in past a child (the one NSH played game with), who grew upto be a look alike of KMJ, and when NSH travels in 2007, he becomes 18 years old KYJ a perfect age for a University student, hence perfect age for HJH boyfriend. So when NSH who is KYJ has plane crash accident, HJH travels back in time and meets NSH who was unaware at that time he will also travel in time, hence the KMJ photo he kept  from past as well as in future, so it is loop of future HJH traveling back in past in KMJ body to meet NSH who becomes future KYJ. 

The length it took for you to write this comprhensive explanation was about 6 or 7 episodes for me to finally get my head wrapped around it, and still I have to focus. Using 4 charcters to portray the time travelers is confusing as all get out for most viewers, but it's kept me entralled. Thank you for providing the details.