An Equity Swap, either a Price (PRS) or a Total Return Swap (TRS), contract is an agreement where cash flows are exchanged between parties where the first party makes payments based on returns on a single equity and the counterparty makes payments of a fixed amount and/or floating amount or payments based on the returns of the notional amount of the contract.
An Equity Option contract provides the right, but not the obligation, to buy or sell a quantity of stock, at a set price, within a certain period of time or at a specific point in the future. This right is monetised through the exchange of a cashflow called the premium, which in turn impacts the pricing of the strike price of the option which is payable/receivable on exercise of the option.
Both derivatives can be used to generate or manage exposures to equity positions in similar ways and with similar risks.