According to Marx, socialism is a stage on the way to communism, which is the more advanced stage of humyn organization not yet achieved in China or the Soviet Union, even according to Lenin, Stalin and Mao.
According to Marx, under socialism we have a dictatorship of the proletariat which is a government organized for the defense of survival "rights." Also, distribution goes by the principle "from each according to his/her ability, to each according to his/her work."
Under communism, according to Marx, the government disappears and there is economic cooperation as well. The principle of distribution becomes "from each according to his/her ability, to each according to his/her need."
Socialists and communists existed before Marx. Marx is the single most-respected authority and reference point, but the words "socialism" and "communism" still have various shades and applications, because of the diversity amongst those calling themselves "communist" and "socialist."
Many calling themselves socialist would like to stop with the nationalization of the means of production and not move on to communism. They also often oppose the "dictatorship of the proletariat" in the name of democracy. For example, they supported the imperialist World War I, because the majorities of their countries supported it, while we Marxist-Leninists found World War I anathema to the proletariat, against survival "rights."
Since World War I, there has been a very large split between many calling themselves "socialist" and those calling themselves "communist;" however, to make matters more complicated there are socialists found who would not support World War I today and there are "communists" who would favor doing whatever the majority wants. There are also "social-democrats" who want reforms to imitate the results of socialism while keeping capitalism.
When MIM uses the terms, we use them this way:
1) "Communism"--the classless society with no state of the distant future.
"Communist"--someone who wants to get to communism or the adjective for "communism." Examples include
many tribal societies of the past and in remote areas still living today.
2) "Socialism" refers to that period/stage between capitalism of today and the communist goal. During that
stage there is "dictatorship of the proletariat." Examples are the USSR under Lenin and Stalin or China under Mao.
3) "Social-democrats"--whether they call themselves "socialist" or not, people opposing the "dictatorship of the proletariat"
in practice and hence socialism itself. Examples would be Sweden today.