When it is said that the Fed cut interest rates, does this refer to the discount rate, fed fund rate or both?
It is exceedingly rare for commentators to discuss the discount rate. As such, referring to “rate cuts” typically refers to Fed Funds.
In any event, under normal circumstances, the discount rate is kept at a constant spread to the Fed Funds rate, so they move at the same time.
In practice, the discount rate is an object that derives from other rates (of interest, required, ...), see, e.g. WACC when calculating NPVs.
The FED always talks about (interest) key rates.