Equity Swap is a special type of Total Return Swap

The five generic types of swaps, in order of their quantitative importance, are: interest rate swaps, currency swaps, credit swaps, commodity swaps and equity swaps.
An equity swap is a special type of total return swap, where the underlying asset is a stock, a basket of stocks, or a stock index.
Most swaps are traded Over The Counter (OTC), "tailor-made" for the counterparties. Some types of swaps are also exchanged on futures markets, for instance Chicago Mercantile Exchange Holdings Inc., the largest U.S. futures market, the Chicago Board Options Exchange and Frankfurt-based Eurex AG.
The cash flows are calculated over a notional principal amount, which is usually not exchanged between counterparties.