It's oversimplification. Socialists and communists also struggled with each other. Communists actually labelled social-democrats as "fascists" for some time. Nevertheless, they have a lot in common (used to have even more in those times) - I don't think someone could argue with that. With communists/socialists national socialists shared their contempt to "outdated society", capitalist democracy ("plutocracy"), and they competed for attention of poor, and disappointed, and all embraced strict regulations. It's really depends on what you see as a core part of socialism, but similarities are plenty, both in goals and methods. That's why, for example, Zhelyu Zhelev's historical research on fascism was prohibited across all socialist countries as it was too easy to see parallels.