Brad DeLong points out that the two rates are not the same...
...and you don't hear much about the discount rate these days because that's not a particularly important policy lever.
But that is not how it's always been. As I point out in my RAE article, this was not true very early on. In his Congressional testimony following the 1920-21 depression, Benjamin Strong discussed how banks would borrow from the Fed, and not from each other, to meet any shortfall in their reserves. Marvin Goodfriend, in his 2003 review of Meltzer's history of the Federal Reserve, describes the experience of using the discount rate during this episode as "traumatic" for the Fed, due to the unexpected potency of that particular policy lever. That experience would lead them, in the mid-1920s, to begin relying primarily on open market operations for implementing monetary policy - which, of course, they still do today. Open market operations work on the federal funds rate indirectly, replacing the earlier policy of expanding or contracting the money supply through changes in the discount rate.
This is part of the reason why I don't like it when people try to evaluate the value of a central bank on the basis of some of its behavior in the early years. Such an approach to evaluating institutions completely ignores the role of learning and adaptation.
Friday Night Music: When I’m 64
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