How does the gospel of wealth justify social darwinism?

According to The Gospel of Wealth, every person has to get paid the same amount of money, whereas the idea of social Darwinism  is that only the strongest will survive, so, I bet the way how the gospel of wealth justifies social darwinism is that if everyone will get paid the same amount of money, the strong person won't be able to win as everyone would be alike (reminds of basic ideas of socialism).

Hope that helps!