Both are created by the same producer, Jung Jong-Yeon PD and both are shows that require the cast to solve problems. The only difference is the premise, wherein The Great Escape is when the cast is challenged to escape from wherever they end up, and the Girls High School Investigation Class's premise is the girls are placed in a school where they have to discover its secrets.
It's the same producer (Na Young-Seok). Basically, the same premise of having celebrities work but the difference is one is about a cafe and one is with a boarding house. Both are very relaxing to watch!