Columbia College and Barnard College are undergraduate colleges of Columbia University - located next to one another, sharing each other’s courses, academic and sports facilities, dining halls, libraries (but not housing). Yes, there ARE specific differences/distinctions - but those won’t be a concern to you unless you some day happen to have acceptance offers from BOTH and would need to choose between them.
I don’t know, how the significant the difference in endowments between CC and BC affect their financial aid, specifically to foreign students. (BC is financially independent, while CC is an entity of Columbia U.)