Plot-wise the two movies have superficial resemblance to each other (woman trying to get away from someone with the help of a sympathetic person), but the main similarity is the VIBE. Moody atmosphere, lots of nighttime shots, neon lights. If you enjoyed one of these movies mainly for its vibes, there's a good chance you're going to like the other one.

Both are investigation dramas that are also about reckoning with the past that you'd rather forget. In A Fugitive from the Past, it's the tumultuous time just after Japan lost the Pacific War; in The Last Witness, it's the brutality of the Korean War. Both movies have epic quality about them.

Both deal with the same subject, which is state-sponsored human experimentation in World War II, and how these doctors--supposedly guardians of human life--ended up doing the very thing that is antithetical to their profession.

Both movies are about mistreated children. The titular character in Boy is put into constant danger (thrown in front of moving vehicles) and in that way is physically abused, basically. The children in Nobody Knows are abandoned by their mother. And both have really good child actor in leading role.

Both are about a family of criminals. The main difference is that family members in Shoplifters really care about each other, while the parents in Boy just straight up use their son for their own benefit.

Both are about children dealing with their parents' separation and the changes brought by that separation.

Both feature a main character that faces (potential) discrimination because of their social background--burakumin in Japan and baekjong in Korea.

Both are about two people who fall in love with each other even though they probably shouldn't, since the man is responsible for the death of the woman's beloved.

Both are slice of life stories with a smattering of fantastical elements. Their characters are basically ordinary people with some personal quirks.

Character(s) in both movies is tailing someone, but they end up getting too attached to their subject.

Both drama set in large-scale catastrophe, showing how the characters face ethical dilemmas in life-or-death situation.

Both are family dramas that feature characters of LGBT minority. Both show how they and their families face prejudice from society.