I believe Columbia College is the undergraduate college within Columbia University. Same campus, 116th St.
Much like Radcliffe is a college within Harvard University.
From Encyclopaedia Britannica:
Columbia University, major private institution of higher education in New York, New York, U.S. It is one of the Ivy League schools. Founded in 1754 as King’s College, it was renamed Columbia College when it reopened in 1784 after the American Revolution. It became Columbia University in 1912.
Columbia College was the undergraduate liberal arts school for men until 1983, when women began to be admitted. Besides Columbia College, the university includes two other undergraduate schools (the School of Engineering and Applied Science and the School of General Studies) and the affiliated Barnard and Teachers colleges.
Maybe some of these people can shed some light on the topic (notice anyone missing?):