campus:A campus is an area of land that contains the main building of a university or colledge.多指大学校园,通常用法有on campus, campus life等。
university: A university is a large and diverse institution of higer learning creaed to educate for life and for a profession and to grant degrees. 指综合性大学。
colledge: 通常指大学中的学院,比如:Colledge of computer science and technology:计算机科学与技术学院。这个单词比较常用,例如: I am a colledge student.
academy:通常指某些专门学科的学校或者机构。Academy sometimes used in the names of schools and colledges especially those specializing in particular subjects or skills. 例如:Academy of Science:科学院。Chinese Academy of Algricultural Sciences.