Socialism and communism can mean two things, either it is political ideologies or economic systems.

• As economic systems socialism is the dictatorship of the proletariat, a transitional state where the state still exists but is being run by the working class. The socialist society will eventually develop into a communist society where the state has withered away as have class distinctions, money and wage labour.
• As political ideologies, communism is describing those who wants to achieve a communist society and think the way to do it is through the transitional socialist society, whereas socialism is a much broader term describing those who promotes the interests and liberation of the working class. It encompasses communists, anarchists, democratic socialists and even, if you're being very generous, social democrats.