yeah it is kind of confusing to wrap your head around but (and bear in mind these are marxist definitions laid out by marx, engels, and lenin–someone from another tendency might give you different answers.

• socialism (ideology) is essentially any ideological manifestation of the proletarian class struggle. there were many socialists and socialisms before marx and there are still many non-marxist socialists!
• communism (ideology), or Marxism, is scientific socialism, or the specific formulation of socialism laid out by Marx. all communists are socialists but not all socialists are communists. the main difference between communism and other socialisms is that communism is built on historical materialism (ie, the understanding of history as the dialectic interplay between different sections of society as caused by advancements and changes in the methods of exchange and production)
• socialism (form of organizing society) is the ‘lower form of communism’ under which the state still exists in the form of the dictatorship of proletariat and classes are in the process of being abolished as society one by one sheds the remnants of the capitalist social form
• communism (form of organizing society) is the 'higher form of communism’ under which the state has withered away and classes have been abolished – stateless, classless society operating on 'from each according to his ability, to each according to his need’.

bear in mind that distinctions this fine-grained are only made by like people who are really deep into theory (ie, Book Perverts like me) and that a lot of the time people will use 'socialism’ and 'communism’ in pretty much free variation as fits the Vibe