The USSR purported throughout it's existence to be a socialist state. To understand this position, you must understand the usage of socialism and communism in Marxist thought, which differs somewhat from how the terms are used in popular culture. In the west, communism is typically used to refer to states ruled by Communist parties. However, Marx used it to mean a hypothetical future state for society, where property would be owned communally and where classes do not exist (property is, in Marxist usage, defined as anything that can be used to create profit). Socialism is, in Marx's view, a transitional stage between capitalism and communism. In this state, property is owned not by the bourgeoisie, but instead by the workers. Over time, the class distinctions and machinery of state necessary for this will wither away, and communism will result. The Soviet Union claimed to be socialist, aiming to produce the conditions necessary for communism (though the extent to which they were is arguable). This is what the quote is referring to - Khrushchev was promising that by 1980, the Soviet Union would be in the process of transitioning from socialism to communism.

We only called all those countries behind the Iron Curtain "communist" as a convenient shorthand (and were justified in doing so because they were mostly ruled by a single party which usually proudly called itself the "Communist Party"), but you will notice that the names of the COUNTRIES used a different term: the Czechoslovak Socialist Republic, the Union of Socialist Soviet Republics, and so forth. This is the giveaway, and the answer to your question: the USSR considered itself (according to its own official ideology) "socialist".

What is the difference, you may ask?

For that, you need to turn to the philosophical underpinnings of those countries' (and, in particular, the USSR's) ideologies. That underpinning is Marxism (though as a Soviet citizen, you would reflexively call it "Marxism-Leninism"), and in particular so-called historic materialism, which Karl Marx, the founding father of the Marxist school of thought, developed as a way of looking at how societies and states evolve over time.

To a historic materialist, human history moves through certain inevitable stages: it all begins with an egalitarian primitive hunter-gatherer paradise which mirrors communism at the other end of history, in that the "means of production belong to everyone" and there is no oppression by the state. However, the primitive society at the dawn of mankind has short, brutish lives with no amenities or much in the way of culture and pleasure. Humanity bootstraps itself up to a higher level of transforming natural resources and amassing wealth, going through distinct stages of society, such as e.g. slaveholder society, or feudalism. These are always marked by a ruling class and an oppressed class, and the oppression at some point gets so unbearable that the oppressed revolt and topple the ruling class and install a new society - rinse, repeat. Please note: If this sounds ridiculous, it is mostly because of my criminal oversimplification in a short reddit post - there is more to it in actual Marxism, whatever you might think about the dubious merits of socialism in theory (or the horrible way it was implemented in actual history)!

Now: we are moving up through history, going through a preordained series of class systems, up to present (at the time of Marx) where you have capitalism. Capitalism is extremely efficient and productive: it makes countless goods and makes them well, and delivers them cheaply and reliably, etc. etc. It has come a loooong way from the primitive hand-to-mouth stage of prehistory. The only problem? There is great injustice, committed by the ruling class (the capitalists) against the oppressed (the proletariat, or workers and farmers). You see, the capitalists hold all the land and all the means of production, and that means that they can extract free rent from the proletariat, who only have their labor to sell.

Enter the socialist revolution: the proletariat topples the capitalists.

And this is the most important point with respect to your question: see, even under orthodox Marxist-Leninist doctrine, it is quite readily accepted as fact that you still don't have communism at this point. Communism means everyone has everything they might ever want. Food and other material goods will presumably be produced by robots etc., you are free -- and so is everyone else -- to spend all your time pursuing whatever you might want, from inventing better robots to writing musicals to just hanging out and not doing much.

But clearly, that is not feasible just yet, even with all the complexity and the wealth produced by capitalism that just fell into the lap of the proletarian revolutionaries. Therefore, there will still have to be a "class system" of sorts in place, a form of exercising power over your fellow citizens, and restraining their freedom.

The difference with socialism is that, for the first time ever, the "oppressor" (i.e., the revolutionary socialist vanguard, embodied by the infallible communist party) indeed has the best interests of the oppressed (i.e., everyone else) in mind (in modern political science-speak, we might call them the "benevolent dictator", though I am not sure that would have flown with the party). While, say, the feudal warlord had only one interest: that the world stay forever the way it is, with him extracting the good life from the serfs and having a good time at their expense, the socialist revolutionary actively wants to bring about a time where she renders herself redundant, by hastening the arrival of said Golden Age of Communism. Marx called this the "withering away of the State".

In other words, Khrushchev simply ventured a forecast that within 20 years' time, socialist society would make the final transformative leap to communist society. Such a statement is politically important also because of the implications for the ordinary citizen AS A CONSUMER. Consider the dim awareness of many under socialism at the time that their brethren in the west were so much better off, with better cars, food, household appliances, gadgets, leisure-time activities, and so forth. Promising them communism, within the paradigm of the official teachings, was promising to go forward with one of the most famous pronouncements of Marx: "From each according to their ability, to each according to their needs." It is the promise of endless abundance, brought about by communism's superior capability to produce and deliver anything and everything you might think of - and, crucially, unlike in a capitalist state, you will not have to work for it, kowtow to your employer or master, compromise in any way!

Consider (might the ideologue of the times say) that, while your West German counterpart has a nice Volkswagen while you are still on a years-long waiting list for a Trabant, that westerner is in constant fear of losing it all, if he loses his job, etc. etc. Now, here with us, in socialist Germany, you already have some perks (guaranteed jobs, free healthcare) that they, poor capitalist workers will never have, but we freely admit cars and roast beef and color TV would be nice, too. Here is the kicker: if you help us build that new society (by following the lead of the party's wise vanguard unquestioningly, enthusiastically), then you will hasten the arrival of the Time of Plenty. There is a clear eschatological aspect to this Marxist premise of predestined history, put into the ideological service of a ruling class that wished for a population of docile dupes, which mirrors that of fundamentalist religions, and works equally well in both contexts.