Social Darwinism was a leading philosophy during the mid 1800s. It stated that only the strongest and the fittest would survive and flourish in society, while the weak and unfit should be allowed to die. Social Darwinists believed that the government should not interfere with social ills such as poverty. Their "law of the jungle" attitude is used to justify their beliefs that humans, like plants and animals, should compete in a struggle to survive.
The Social Gospel movement is a Protestant Christian intellectual movement that was most prominent in the early 20th century United States and Canada. The movement applied Christian ethics to social problems, especially issues of social justice such as economic inequality, poverty, alcoholism, crime, racial tensions, slums, unclean environment, child labor, inadequate labor unions, poor schools, and the danger of war
The Gilded Age was a period of economic growth as the United States jumped to the lead in industrialization ahead of Britain. 1878-1889
Both took place around the same time, but each differs in their own way.
One deal with faith while the other was science.
"Google.com" does wonders.