Faith (2012)

Time travel, characters move between past and present. Both are Korean shows. ML feels hopelessly resigned to his fate until he meets the other (ML or FL).

Both are historical dramas with fantasy worldbuilding and elements. Both have a similar feel despite very different plots.

Both have people who time travel and fall in love with someone from a different time.

Historical setting, both are Korean dramas. ML and FL have a strong bond and good chemistry. ML becomes traumatized by the constant war. Surprising hopeful/happy ending after ML is wounded/near death and thought to be dead/possibly dead by FL.

Time travel, characters move between past and present. Faith has a more serious tone but there are similarities.

Time travel, characters try to change fate. Bittersweet but happy feeling ending. MYG is short length, while Faith is full length, though.

Both have female lead time travel
Both havd a struggling romance with happy end
Male lead falling in love first

The story content is different but both of the girl in the story went through time travel back to the past time.