They both have mothers trying to handle the balance between supporting their children and existing happily. Hi Bye, Mama has more dark and serious themes whilst Doctor Cha is slightly more comedy focused.
Both main characters are teachers in schools where power lies with the students who have powerful relatives. Both end up changing the dynamic of the school with their bizarre personalities.
They both have elements of the husband going to an alternate universe or time which was caused by a single change in the man's past actions.
It has the same concept of having supernatural beings (ghosts and vampires) investigate crime and law-related activities.