As you can imagine, politics is often complicated by a very partisan and politically/historically illiterate approach to definitions.
Socialism, like other political terms, is a broad classification which allows for a considerable degree of variation in practice. What makes a socialist society "socialist" is "public ownership" of the "means of production". Socialist politics attempts to create an egalitarian society by "sharing" ownership of industries which typically are owned almost exclusively by an aristocratic elite. Socialism is a political response to inequality.
It's worth noting that Communism is a variety of socialism where society is governed by a one-party state, whose purpose is to lead the people towards greater equality. Considering that Lenin said: "Communism is Soviet power plus the electrification of the whole country" ... it's fair to say the exact definition can vary considerably.
There are many different examples which are relevant to contextualise the point. The Soviet Union is the most famous, but even within Soviet history there were arguments about how society should be organised. The USSR switched between leaders who, generally speaking, prioritised the survival of the state (Stalin, Brezhnev) and those who prioritised the empowerment of the individual (Khrushchev, Gorbachev). Lenin even proposed the "New Economic Plan", which advocated the Communist state's industry should become for-profit. Stalin disagreed.
Lenin believed, without global revolution, the Communist state had to be pragmatic and manage capitalism over the long term to survive. Stalin believed that, without global revolution, the Communist state needed to rapidly industrialise to provide the military-industrial capacity to protect its short term survival.
What's interesting here is that Mao's policies were essentially Stalinism for peasants, but after his death China's Communist party adopted the NEP under Deng Xiaoping's leadership. All of this is socialism, because the means of production is owned and run by the state, (in principle) for the benefit of the people.
Communism is a top-down system, where the leadership make decisions which must be obeyed by the people. The two main alternatives, Democratic Socialism, and Anarcho-Syndicalism, represent other ways of distributing power.
The simplest way of describing the difference is to say that in Communism power is given to the Party, in Democratic Socialism power is given to the voters, and in Anarchism power is given to the workers. Again, these are all legitimately socialist systems, just governed by different philosophies.
After the Second World War the United Kingdom voted for the socialist Labour Party. Their policies were to nationalise many industries (coal, steel, transport, healthcare, defence, etc) and create public housing after clearing the slums. This was the socialism which George Orwell wrote 1984 and Animal Farm in defence of, in opposition to Stalinism. British socialism came to an end with Margret Thatcher's election victory in 1979.
The Labour Party became "New Labour" with the abandonment of Clause IV in 1995. This clause in the party's constitution made the party socialist, by requiring the public ownership of the means of production, and without it Labour transitioned into a Social Democratic party.
Venezuela's economy consists of a large public sector of nationalised industries, in an attempt to create an egalitarian society. That's quintessentially socialist. However, Venezuelan Socialism appears to be transitioning from a Democratic Socialism which emphasised the empowerment of the individual, into something more Stalinist, which emphasises national survival. It's all socialist, but whether it is any good is another question.