Columbia vs Columbia University

Columbia and Columbia University both are nouns.

Word	Noun	Adjective	Verb	Adverb
Columbia	Yes	No	No	No
Columbia University	Yes	No	No	No

As nouns, Columbia and Columbia University are synonyms defined as:

Columbia (noun)	Columbia University (noun)
a university in New York City	a university in New York City
capital and largest city in South Carolina; located in central South Carolina
a university town in central Missouri
a town in west central Tennessee
a North American river; rises in southwestern Canada and flows southward across Washington to form the border between Washington and Oregon before emptying into the Pacific; known for its salmon runs in the spring