Back in the 19th century—before the working class was split into the factions of socialism, communism and anarchism—these words and their movements were often used interchangeably, with socialism meaning something along the lines of “the people own the means of productions”, communism describing a society that follows the paradigm of “each according to their abilities, to each according to their needs” and anarchism meaning that no instance of anything should rule over others.

As you can see, these ideas were not contradicting each other but rather focussing on different aspects of the liberation of the working class