Communism is the ultimate dream-a classless, government-less society which exists on the principal of "From each according to his ability, to each according to his needs". It is a cooperative society with everyone working together to produce what they need without trying to exploit one another. Marx argued that the pre-industrial society was a primitive communist one as well. We can quote the Medina society and the later Ottoman Empire in this as well. They shared several characteristics with what one theoretically would want in a communist state (NOT socialist). The Byzantines also tried really hard to make a "communal state" where resources were shared and work was done to eliminate class inequalities. If we go further back in human history we will find that many of the earlier civilizations had very few classes, mainly just a leader who was either a distinguished military commander or a religious authority (or considered divine somehow) and everyone else and the people worked for the community's benefit.

Socialism is supposed to be a transitory stage. I've mentioned the two properties of a socialist state before but I'll repeat them again. The government is still in control but they work for public benefit, not for the benefit of the rich, and the resources are being re-distributed in society to reduce the class differences. It is what is practically visible today though it itself has many many forms.But the basic differences between the two have been outlines above. I hope this helped.