While there many credit reporting agencies, or credit bureaus, there are three major credit bureaus in the United States. They are Equifax, Experian, and TransUnion. These bureaus are all publicly-traded, for-profit companies who are not owned by the government. However, the government does have legislation, the Fair Credit Reporting Act, regarding how these and other credit bureaus should operate.
FICO, the company who developed and maintained the FICO Score is not a credit bureau. While they compile your credit score based on data from the major credit bureaus, they do not collect credit report data on their own.