Monster (2014)

Both protagonists are out to save a little girl, both stories are full of blood and violence, and both stories have an amazingly hot guy.

Min Ki is also the lead in this one. A lot of blood and violence.
It's a dark-action themed movie about the lead who, because of a match fixing scandal, gets into trouble with shady loan sharks. He finds himself stuck in an amazingly violent underworld and sees no easy way out. He struggles with love and friendships because of his new job as a loan shark and ends up losing those near to him.

Here's the trailer: https://www.youtube.com/watch?v=_nIo7spkviQ

Both movie have same kind of concept. A boy is forced to became a monster. If Hwayi: A Monster Boy presents the story of a 'not-wanna-be-a-monster' boy, in Monster, the lead became a monster by his own choice.

Both movies are very similar. Both have strong woman. But in monster, the woman wanted to get revenge from serial killer.

Kim Hyuk lives a fast life as a high-ranking mobster in the port city of Busan, South Korea. His closest friend is fellow mobster Lee Young Choon. Even though Kim Hyuk seems to be on top of the world, he is haunted by the memory of leaving behind his younger brother, Kim Chul, and mother as they attempted to flee into South Korea from North Korea. Kim Hyuk's mother was beaten to death, and Kim Chul was imprisoned after they were caught by North Korean authorities.

Kim Hyuk then travels to Thailand with new gang recruit Jung Tae Min for a meeting with Thai gangsters. The meeting turns out to be a set-up, planned in part by Jung Tae Min. Kim Hyuk is able to shoot his way out of the meeting, but he is later caught by the Thai police and imprisoned. When good friend Lee Young Choon hears of what happened to Kim Hyuk in Thailand, he goes to the Thai gang's holdout in Pusan to kill their boss. During the shootout, Jung Tae Min is shot in the leg.

Three years later, Kim Hyuk is finally released from prison and travels back to Busan. He finds his close friend Lee Young Choon washing cars now and has a limp leg. Jung Tae Min, the man that betrayed him, has climbed up the mob ranks and is now a feared crime boss. Furthermore, Kim Hyuk's younger brother Kim Chul has arrived in Busan and works for the Busan Police Department. Meanwhile, Kim Chul keeps close tabs on Jung Tae Min as he attempts to take down their gang.

When Jung Tae Min attempts to take out Kim Hyuk's younger brother, Kim Hyuk throws himself back into the gang world to exact revenge.

It's a story of a young woman seeking bloody revenge on a psychotic man who killed a member of her family.

The stories are very different but the way the story is executed cinematically actually feels similar and they both uses the nuances of dark comedy pretty well. Both are great movies and contain some of the most graphic gore scenes in a movie anywhere.

While this may not have a "psychotic killer chases witness" premise, there's the cat and mouse element between an innocent civilian and a serial killer and the chase is really thrilling. The fight between the main characters in "Monster" was a more exciting one in my opinion, however both were entertaining to watch.

They both star Lee Min Ki in a darker roles.
They both are great suspense/thriller movies.
The difference is that A Million is a game show and Monster is a revenge story.