Both FLs pretend to be eunuchs to stay by the emperor's/king's side. Both MLs have an initially cold personality but are very loving, both FLs are high-spirited.
Both are historical dramas in which the ML is a king and the FL is his servant or working for him in the palace. Both have a scene in which the bad guys suspect the FL's identity and abduct/torture her and the ML arrives to rescue her.