Both are music themed Korean BLs.
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The Red Sleeve tells the story of the son of Sado who is the main focus of Crimson Moon.
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Both have an environmental message and focus on the relationship between a mermaid and a human.
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Both have the same actress as one of the FLs and are about the relationship between a human and a mermaid. Both have censored/implied GL vibes.

Both FLs have their faces exchanged with another girl and are believed to be dead, and both are on a quest (to solve a mystery vs. revenge). Both MLs are mysterious figures who the FL initially doubts.

Both are historical/fantasy dramas that involve a seeming magical ability to exchange faces between different people.

Both FLs are face swapped and believed to be dead. Both MLs recognize certain mannerisms/behaviors in the FL, leading them to question her identity.

Both FLs are face-swapped by another woman for her own goals. Both FLs have a past connection with the ML who recognizes certain distinct things about the FL that reminds him of her true identity. Both MLs have a frightening aura about them but are very loving toward and deeply in love with the FL.

Both are historical dramas with a similar slower pacing and vibe. Both follow the ML, born into poverty, who suffers hardship and escapes death as a child and young man, and ultimately becomes a fighter for the people against the evil rulers. Both FLs are the MLs' second loves.

Both are short length dramas that involve a married couple with a cheating, evil husband, and a magical swap between characters due to a mirror.

Both FLs are strong martial arts masters who accidentally harm the rich CEO ML or his belongings and end up involved with them as a result of paying off that debt.

Both are mini dramas in which the wealthy, city ML is trying to get out of an arranged marriage made by his grandparents with the country FL, only to fall for her.