The Discount rate is the rate of interest at which the Fed Reserve lends money to other commercial bankers.
The Federal Funds rate is the rate at which the commercial banks lend overnight money to each other.
The commercial banks borrow money from the central bank against a host of collateral like commercial papers, mortgage based securities, and asset based securities.
However most of the banks are reluctant to approach the central bank discount window for borrowing funds. This is because the commercial bankers do not want to send a signal to the market that they are not solvent enough to attract funds from the open market.