As opposed to currency derivatives, interest rate derivatives, commodity derivatives, and so on. An equity swap typically involves an "equity side" of the transaction AND something else, like interest rates or oil prices.
Equity derivatives can be written on indices (e.g., the S&P 500, the FTSE-100, NASDAQ) as well as on stocks. In fact, they are often bought "out of the money" by mutual fund managers as insurance against a catastrophic decline in the fund value.
--Dykema Gossett & Andrew H. Connor "The poison pill resurgence," Lexology (15 March 2010)