A credit report is all numbers. The credit report includes various financial information gathered to develop a credit report.
Here are some examples of information that's in a credit report: Your Name (including any prior names or aliases); current and previous addresses; your employers past and present; revolving accounts; installment loans and the loan status; open and closed bank accounts; account payment history including utilities; recent credit and loan applications; collection accounts (any accounts that are being handled by a collection agency).
A background check includes the credit report plus other information such as criminal history. It can include other information as requested by a landlord, such as any record of previous evictions or lease violations. The background check can be limited to information on a state database or the report can be expanded to include national and even international searches.