What's the difference between 校园 (meaning "campus") and 校院? Is 校院 incorrect?
They refer to different things.

校园 means campus/schoolyard.

校院 means 校 and 院. In most cases they mean 学校(school) and 学院(college/academy/institute), e.g.


  校院简介
  本人在华并未以侨生身份申请其他大学校院。
  实行校院两级管理体制是高校深化体制改革的一项重要措施。


According to the context, they might mean 学校 and 医院, e.g.


  “校院合作、工学结合”是我国卫生高等职业教育改革和发展的必然趋势。


PS: 校院 is infrequently used because we have another much more common word 院校 (学院 and 学校). 校院 seems to be used only when the order does matter. E.g. in 校院简介 and 实行校院两级管理体制, 学院 is considered as the lower level unit of 学校, then 校院 should be used.