Girl falls first

Go Go Squid

FL is still in college, ML runs a cyber something club and wants to win a championship. They share a fluffy romance. FL falls for ML first but he rejects her. There is also some I'm older than you I cant fall for you thing that the ML is conflicted with.

Prime Minister and I 

My Princess

Another Miss Oh 

Girl who sees scents 

Wedding (2005)

Attic Cat 

Warm and Cozy 

Secret Life of My Secretary 

Master's Sun 

Buzzer Beat 

Moorim School (Second couple)

Coffee Prince 

Rich Man, Poor Woman (Korean Version)

Full House (Thai Version)

Our times (Taiwanese movie)

there's also it's okay that's love and it's a 10/10 drama but it's the opposite, the man is heads over heels for her, she's different than the women he used to date, he's a player but she puts him in his place, he'll go for her though 

the chemistry between the male and female lead is crazy, and it's a unique drama, I highly recommend this, I also saw someone mentioning another oh hae young, this one is very good as well, these two unlike heart strings and the liar and his lover, have a story, a very strong one, they'll get you hooked 

 Aseel :

there's the liar and his lover, she wasn't pathetic but she was gullible , it's not my preference but it matches with your description and it's very light and simple, a better one I'd say is heartstrings, she liked him in the beginning but then when he rejected her, she moved on, and then he started to like her, it was one of my favorites 

Heartstrings sounds exactly what I'm looking for, thank you!

Love revolution: the second "couple" is like this. The reason why I put quotes is because it's left open at the end so hopefully, there will be a second season. The girl who is friends with the female lead likes the second male lead who is a bad boy but he doesn't know. He likes the female lead but doesn't want to pursue her because his friend (male lead) likes her. They have a cute dynamic.

Dr romantic season 2:  The second couple is also similar to the main couple from a poem a day. It's between a doctor and a nurse. The girl is really sweet and adorable and the guy is a little reserved because he got heartbroken. They make a really cute couple. 

The secret life of my secretary: The second couple again lol. The girl is really rich and likes the second male lead. She pursues him very confidently and he rejects her because he thinks she is playing with him.  He thinks she has a relationship with his friend but it was just a misunderstanding.