Lou

Both dramas are centered around a girl who is willing to do anything and everything to get her revenge. Both girls can be described as anti-social/sociopathic beings.

Both dramas revolve around a girl who was as gifted as her father. As a child they got separated and they did not have any contact. Both girls try to avoid being confronted with their inherited gift. Both women's fathers are very successful and well known for what they do. Then a death due to a serious illness brings them back into the orbit of their father and both they have to find a way to proof their gift.
In both dramas these girls are meeting old acquaintance of their father who teach them both all that they know.
There are additional similarities in regards to family dynamics but these would reveal too much.

Still it is basically the same story just in Drops of God the story revolves around wine, while in Miss King it revolves around shogy.

Both female leads are stated in the drama that they are sociopaths. Both females have the help of 2 MLs to achieve their goals. In both dramas one ML knows and gives himself the fault of her turning into who she is.
The biggest difference is that Dear X is very dark while Confidence Queen is more light hearted and fun.

Both female leads are willing to do anything to receive an advantage in their goal. Both dramas revolve around the entertainment industry and both FL use the ML to their advantage and manipulate them to help them achieve their goals.

Both women suffered abuse/witnessed a crime that made them vow to themselves to improve their standing in order to never be in the same position again. In doing so they meet male leads with which they grew up, that know (nearly) all their dark secrets and are willing to help them and stand next to them to help the FL achieve her goal even when they are morally not always supportive of their actions. Both female leads lack empathy and show some sort of sociopathic tendencies.

Both female leads are surrounded by domestic abuse and both receive an opportunity to change their situation. Both women do not hold back and are willing to do anything and use anyone to keep their position and climb higher. Both get help from males that they use to their advantage.

Both dramas revolve around women that are willing to do anything to achieve their goal and reach the top of the top. They both get help by men that are willing to let themselves be used by these women in the hopes of maybe changing them at some point. Both men then decided on similar outcomes.
Both dramas have a murder case woven within the story.

Both dramas offer a group of people that get together and revenge people that got taken advantage off. Both are more light hearted, funny, focused on family(friendship but with serious and more darkish undertone.

Both dramas revolve around a woman that experienced a brutal crime as a child/teen and lost her family because of it. Both girls are receiving help form a male that knows their secret past. Both girls take on a false identity to take their revenge against the ones that hurt them.

Both dramas deal around money/an object that brings a lot of money (drugs) and in both dramas specific people lose it, and are now willing to do anything to require it.

Both dramas are done by the same screenwriter. In both dramas the "happy" life of the woman gets interrupted by something that has happened to her husband. She then teams up with the male lead to resolve the situation. Both male leads at some point are faced with similar situations where the police looks for them.
Overall although there are strong differences, such as the male lead working for the police in Lies within, while the ML from Walking on Thin Ice is involved with the drug world, they are having very similar situations and themes.

Both dramas deal around two housewives that are confronted with a difficult situation and need money. They stumble accidentally across a situation where they are confronted with a solution to resolve all their financial problems. However in taking that solution they get intertwined with the world of drugs.
Both meet a male that they team up with to help resolve both their problems.