In what way was communism a reaction to socialism?

While socialism looked at helping everyone and limiting the distribution of wealth, communism became some sort of extreme socialism where complete wealth redistribution was a primary goal. In socialism, there were still social classes and stratification along the lines of social classes, while communism sought to abolish the classes completely and make everyone have the same amount of resources or manufactured goods. While it was possible to become wealthy or a part of the rich part of society in socialism, it was not during communism and such behavior was severely punished.