The policies of Social Darwinism and those of Progressivism have several similarities and differences. And although now they appear to be extremely distinct, they had more of an overlap in the past.
Social darwinism was the idea that humans are subject to the same rules of natural selection than animals and plants. This view stated that some races and social groups are less "fit" than others by nature. This was used to justify controversial practices such as imperialism and racism.
On the other hand, Progressivism is the idea that society needs to improve, in particular when it comes to helping those who are less fortunate. Progressives wanted better labor laws, a safety net, healthcare, etc.
These two views differ from each other mainly in the view they take of the "lower classes" of society. While Social Darwinism believed that these people were at the bottom of society because of a natural law, Progressivism argued that this was in fact a consequence of social injustices.