The buyer receives the notional amount times (realized volatility − strike). The strike is quoted as volatility, such as 30%, and the notional is an amount per volatility point.
Consider a hypothetical example in which the strike is 20% and the notional is 1 million yen per volatility point. If realized volatility is 25%, the buyer receives 5 million yen. If it is 15%, the buyer pays 5 million yen.
It differs from a variance swap in that the payment is a linear function of volatility. The fair strike of a volatility swap is lower than the square root of the fair strike of a variance swap (the variance value). Unlike a variance swap, a volatility swap has no simple replication method (according to a 1999 Goldman Sachs paper), and its valuation depends on an assumption about the volatility of volatility.