Both dramas are about identity swaps in a gender flipped version of each other - in TOD, a bandit is engaged to a princess who he thinks is a commoner/bandit, and in YTFJ a bandit is engaged to a lady who thinks he's her judge fiancée who he's posing as. Both dramas have a fun tone and don't take themselves seriously.

Both are short length dramas in a Republican Era setting with a domineering ML. One has fantasy elements and the other doesn't, though.

Both are short length dramas with a modern day FL entering the world of a historical novel. The couple is originally antagonists in the story.

Both dramas have a modern or future FL entering a fictional historical world. Both MLs are villains who the FL becomes entangled with.

Modern day FL enters a historical fictional world, and falls in love with the antagonistic or villain ML.

Both are short dramas in which the FL enters the world of a story and ends up altering the plot, sometimes intentionally. She also ends up falling in love with the villain of the story.

Both are short length dramas with a real world FL entering a fictional historical world where she must change her fated death and survive. Both have antagonist/villain MLs who the FL falls in love with.

Both are short dramas in which someone from the real world enters the world of a story and must change things to survive which leads them into a relationship with the villain.

Both are short length dramas with a real world FL entering the world of a novel and falling in love with the story's villain.

Both are short length dramas with a real world FL entering the world of a historical novel and falling in love with the story's villain.

Both dramas have a real world FL entering the novel and trying to change her character's fate since her character is supposed to die in the story. The FL in both is married to and falls in love with the story's villain who begins to change as he falls in love with her.

Both are short length dramas with a real world FL entering the world of a novel and falling in love with a character in the story. Both have guides who give them tasks, and both FLs must change their fate and survive to get home.