The payment depends only on correlation and is not directly affected by the size of each stock's moves. It is described as a transaction similar to a variance swap1.
Consider a hypothetical example with a notional amount of 100 million yen and a strike of 0.5. If realized correlation is 0.6, the buyer receives 100 million yen × (0.6 − 0.5) = 10 million yen. If realized correlation is 0.4, the buyer pays 10 million yen.
The profit and loss of a dispersion trade includes a part from volatility as well as the correlation spread. A correlation swap differs in that it has no such part1.