Immortal (2021)

Wang Won’s father is the king of Goryeo while his mother is the Yuan emperor’s daughter. He was born with many gifts as he has good looks, the wisdom of a snake, and a magnetic personality that draws people to him. But behind his gentle, virtuous demeanor, he has ambitions to conquer other lands. He has a faithful friend named Rin, who is a royal cousin and comrade with the same ambitions as he does. Then Wang Won has an encounter with a young woman named, San. San was someone that he recalled having met when he was a child and was lodged in his mind ever since. Wang Won sees how bright and confident San is and befriends her as well. But this friendship plants the seeds of tragedy. San’s beauty mesmerizes both Won and Rin and their seemingly strong bond start to fray over one woman…

The series tells the story of a man-turned-immortal, Bulgasal, who wants revenge from a woman with a mysterious past and present, who he deems responsible for his immortality and miseries from the past 600 years, hoping to free himself from his curse.
?

It is believed that when a person dies, their soul spends 49 days in Jungcheon, or Purgatory before their eternal fate is decided - heaven, hell or rebirth. That's where accomplished demon hunter Yi Kwak finds himself as he lies on the edge of death in our world. Blessed with astounding swordsmanship and the uncanny ability to see the evil spirits invisible to most, Yi enlisted with the royal squad of elite demon exterminators, the Chuhyongdae, following his fiancee's tragic death. In Jungcheon, he finds Yon Hwa again, but she does not recognize him - she is a spirit of the afterlife now, severed from earthly memories. Moreover, she is deeply entangled in a great war between the white-clad warriors of reincarnation and a swarm of dark spirits determined to forever shatter the cycle of life and death. The battle is desperately close to a terrifying conclusion, so Yi must draw his sword to defend the woman he loves and all they hold dear - and confront the same soul that was once like a father to him.

The only similarity is that they are reincarnated lovers and both think that the other one destroyed their family.
Both dramas are very very different from each other except the reasons above. While bulgasal is a revenge, suspense, thriller drama with a little bit of Melo and romance, "from now on showtime" is a rom-com, lighthearted drama with some ghost and revenge plot.
But both are very interesting drama. Even when Showtime is still on air i recommend it cuz its not looking like it will disappoint it's viewers, and am loving it do much.

859 AD. The once-great Tang Dynasty is now declining. Numerous rebel groups have formed, the largest of which is the House of Flying Daggers, based in Feng Tian county. They steal from the rich and give to the poor, gaining the support of people. The local deputies have managed to kill their former leader, but the rebel group only becomes stronger, due to a mysterious new one. Jin and Liu, two police captains, are ordered to kill the new leader within ten days.

Cho Yeo Hwa has been a widow for 15 years. Her in-laws are the most prestigious noble family in the kingdom. During the day, she leads the life of a widow devoted entirely to her dead husband's memory and rarely ventures outside the gate of her home. At night, Yeo Hwa dons the mask of Hero, who secretly jumps over the surrounding wall to save the helpless. In the process, she crosses paths with Park Soo Ho, a handsome senior officer in the Capital Guard, who quickly realizes that Hero and Yeo Hwa are not who or what they appear to be.

-similar plot about reincarnations and meeting people from your past lives
-romantic plot is more fleshed out in CT
-Bulgasal is a more slow burn mystery of the past than Chicago typewriter, but CT also has a mystery of the past the characters are tying to unveil
-bulgasal is more fleshed out in the fantasy aspect
-CT has similar wholesome character relationships like Bulgasal, but in CT they're more friends based than the found family troupe in BIS
-angsty, aesthetic and bittersweet. The osts in both are amazing, acting and cast and cinematography are great in both.
-Both of them are different in terms of setting and time line, CT is more political and set in 1930s Japanese occupied Korea.

Historical and fantasy themes are similar
Beings other than humana
AATM has a more direct romance
Both have ongoing mysteries of the present and past
BIM has concepts of next lives and reincarnations as a major theme, but it's more of a minor one in AATM
both are fantasy based mysteries, AATM set entirely in the historical Era.

Both series are very much a mixture of folklore, folktale, legends, and myth. This aspect differentiates two series from others tagged with a combo of [Mystery, Thriller, Drama, and Fantasy].

The series tells the story of a man-turned-immortal, Bulgasal, who wants revenge from a woman with a mysterious past and present, who he deems responsible for his immortality and miseries from the past 600 years, hoping to free himself from his curse.