The Devil Punisher (2020)

I found the plot with the villains of both dramas being very similar - both hold high positions in the community therefore no one suspects them, but behind the scenes, they take advantage and do shady things. Also, the whole supernatural background was a bit similar.

Quiet and gentle, Min Jae Yi is everything a good daughter of a prominent family should be. Engaged to the son of the Second State Councillor, Jae Yi knows that the only way to bring herself and her family honor is to accept her fate, which she does with grace and charm. Devoting herself to learning everything she needs to know to become a good wife and mother, Jae Yi dutifully prepares for the future. Sadly, destiny has other plans for her future. Four days before her wedding, Jae Yi’s family is murdered. With no one else to blame for the unexpected tragedy, Jae Yi soon finds herself the object of baseless and horrifying accusations. Blamed for the death of her family, Jae Yi might not have had much of a future at all, if fate hadn’t decided to intervene. Bringing the lonely crown prince, Lee Hwan into her life at just the right moment, Jae Yi is saved from a dismal fate, but her salvation comes at a price. Plagued by a mysterious curse, Lee Hwan agrees to help Jae Yi, but only if she agrees to help him break his curse in return. Unable to refuse such an offer, Jae Yi agrees to the prince’s terms, setting them both on an unexpected path toward love. But what chance does their love have of surviving when one of them is a former murder suspect and the other is a cursed prince?

Both dramas are Chinese mythologies where a deity decent to the mortal world. One of them is a Taiwanese drama whereas the other is a Chinese one. Both have some supernatural elements and are fantasies.

I found myself wondering if The Devil Punisher was not a remake of Goblin. They have somewhat of a similar esthetic (though Goblin is much better made); look at how similar the show posters are!
If you like stories about ghost fighters and amnesia, then you'll love Goblin.

Both dramas are about gods and deities navigating modern world. While Devil Punisher is heavier on the ghost aspect, both series have a major romance plot as well.

Hua Xiao Xuan is a witch of a supernatural flower shop called "The Memory Garden," where she helps her customers let go of their fixation and move on with their lives. One day, she meets the man who accidentally stole her sense of smell during her 13th regeneration years ago. The sense makes him immune to her powers and allows him to enter her shop without invitation. She foresees their lives intertwine and the darkness she is fighting against may cause his death someday.

A baker by day and demon fighter by night, Zhong Kui, a reincarnated deity must jog his amnesiac lover's memory of their millennium-long romance.