Ashi Girl (2017)

Both dramas have a modern day FL who finds herself in the past where she becomes involved with the ML. Both dramas are relatively short.

Both are mini dramas with a modern day FL who finds herself in history.
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Both revolve around time travel and love. Both takes places in the Warring States Period, one in Japan (Ashi Girl) and other in China (A Step Into The Past).

Both are relatively short dramas about a modern day FL ending up in the past, meeting a soldier/general, and falling in love with him.

Hayakawa Yui is a 16-year-old girl whose only strong point is her ability to run fast. When her reclusive but genius younger brother invents a time machine, she accidentally gets sent to the Warring States era and meets the young lord of the Hagi clan, Hagi Tadakiyo, and falls in love with him. Upon returning back to her modern time, she discovers from her high-school teacher that the Hagi clan are doomed to be wiped out in history. Desperate to save this young lord, she finds her way back to the Warring States era, and so her adventure there begins.

Both are mini dramas with a modern day FL who finds herself in history.
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Both are shorter length dramas in which a modern day FL travels back in history. Both MLs are in the military (general vs. soldier).

Modern day FL time travels to historical time, meets and falls in love with ML.
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Modern day FL time travels to the past, meets and falls in love with historical ML. Both are shorter dramas.

Both are dramas with a modern day FL who time travels to the past and falls in love. Both FLs mess with history, changing the fate of the characters/historical figures around them.

Similar feel and tone, featuring a time traveling character between historical and present day with a historical ML and modern day FL falling in love.

Both are time travel comedic fantasies where a present-day student is magically transported back into the Warring States period and into the life of an important but not famous person from history, and realize they have a mission to help this person.

Both are mini dramas with a modern day FL who finds herself in history.
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One is the original series, the other a bonus epilogue that concludes the story. While the original drama has a closed ending, the epilogue adds a bit more and has a sweet, happy ending as well.

Female leads are highschoolers, who have no interests in studies before time-traveling in the past. The atmosphere is light-hearted and funny. Both have cute and fluffy romance with female leads hiding their gender. While one drama is Japanese, the other is Korean.