Both are basically a gender swapped version of the same plot - one of the leads is a bandit who first meets the other noble lead while the bandit is in disguise robbing them. Later on, the bandit lead switches identities with another more powerful person who is missing (a judge vs. a princess) and becomes engaged or married to the noble lead. Their identity is eventually revealed but by then the two have fallen in love.
Both are mini dramas with an upper crust FL who is already engaged to a scholar/scholar-type when she becomes entangled with the ML who is a bandit using a false identity. Despite his roughness around the edges and them clashing at the start, his good heart makes her slowly warm to him and the two fall in love.
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.