'Building socialism' and 'actually existing socialism' are pretty much synonyms, because the terms for the transition stage between capitalism and communism are vaguely defined.

Some call the end point of a "classless, moneyless society" communism, some call it socialism - and some call the transition period, where a society still has features of capitalism alongside features of communism, socialism.

Ultimately it comes down to: who holds political power in a given society, how strong is their grip on it, and how forcefully are they pushing in the direction of communism?

For myself, I would use the word 'socialist' for any country that's somewhere along the transition stage, with whatever features are peculiar to that particular country's history, as long as it's controlled by a Dictatorship of the Proletariat led by committed communists.

So for instance, I would call the USSR, China, the DPRK, Cuba etc. "Actually Existing Socialism" whereas countries with 'socialist policies' (basically, pro-welfare and pro-development) but no DOTP like Venezuela are less clear. Conversely, imperialist nations with big welfare states, like Norway for example, despite being called 'socialist' all the time in the capitalist media are very certainly not.

It depends on how you define socialism vs communism – a question to which there is no right answer, coz it's a semantic convention.

In Lenin's terminology, they were (actually) socialism and building communism (a classless society)

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I can only agree with what others have already said on this. This is primarily a question of terminology. For us MLs what we usually mean when we speak of actually existing socialism is a state that is in the transitionary stage between capitalism and communism in which the society is being developed and guided toward communism under the dictatorship of the proletariat.

Building socialism or socialist construction are essentially ways of saying the same thing and i personally prefer using these terms because they emphasize the fact that this is an ongoing process, it is a movement towards something and not a static state. I like to say socialism is something you do, not something you are or have.

There is no timeline that says how long this process will or should last as that depends entirely on the material conditions of that specific society as well as on the external conditions in which that society exists (in the present global context limitations are imposed on the development of AES states toward communism by the dominance of neoliberalism and the threats of neocolonialism and imperialism).