Talking about the socialism the economic system, where the government runs and controls the production resources, was owned by the society to achieve a common good.
If we talk about the Progressivism part, the political philosophy that raise the standard of living of the members of society was to achieve a positive social change.
Comparison:
Both have the perspective that economic and political equality but they differ in their views and approaches.
The Socialists wanted to abolish capitalism and took advantage of working class.
The Progressives want to employ capitalism to benefit the masses and wanted a regulated business environment.
Hope this helps.