The common thing between Socialism and Anarchism is that they are both Utopian. These two ideologies talk about societies that are hypothetical, a form of society that can be attained only in theory. And along with these two social theories are the means by which men tried to utilize to attain what these ideologies represent. Unfortunately, what is happening is that every time men would try to push for it, the means to attain it collapses in chaos and the goal is always left far from reach.
However, though the two share the same characteristic (both are unattainable), they differ on the means by which they are tried to be achieved. Socialism has this notion that a concentration of power to a few individuals or groups would bring the goal. On the other hand, Anarchism says that the goal can only be attained if the concentration of power is dissolved.