Yes, you're right. The federal funds rate is usually a fraction above the discount rate, but they move together. Because the Fed views using discount rate funds as a bad reflection on the borrower, the borrower will use the federal funds borrowing if possible. I've even known banks to borrow from big customers (Eli Lilly) overnight to avoid going to the window.
In the United States, the federal funds rate is the interest rate at which depository institutions (banks and credit unions) lend reserve balances to other depository institutions overnight on an uncollateralized basis.
From: https://en.wikipedia.org/wiki/Federal_funds_rate