So there's a decent amount of variety depending on what point of Soviet history you're talking about, so I'll take the time and focus on the initial construction of the Soviet Union, and how Lenin's (and the other Bolshevik's) application of Communism differed from Marx's theory.

The first, and most glaring difference between them is one that Lenin had 'relatively' little control over, that being the split from Historical Materialism. Historical Materialism has a few faucets, but the relevant one here is how it/Marx describes the progress of history. Marx developed the concept that there were various stages of history based on the mode of production which was more prevalent, and that Communism required a period of Capitalism to develop the Proletariat and the means of production needed. In essence, Marx believed that Communism could not occur without the Bougeoiuse overthrowing the previous Aristocracy, developing a capitalistic society industrializing the nation, and enlargening the proletariat until they made up the majority.

The October Revolution did not fit into this paradigm. The February revolution had only just done away with the Monarchy/Aristocracy, and by the October revolution, the majority of Russians remained rural peasants with little in the way of a Capitalistic class. As such, the Bolshevik's (mainly Lenin's) decision to go forward with couping the Provisional Government was against Marx's concept of how and why a Communist revolution should occur. Members of the Bolshevik's central committee Zinoviev and Kamenev voted against the proposal for immediate insurrection for this very reason. The lack of a period of Capitalism leading into the Communist revolution is perhaps one of the largest differences regarding Lenin's application of Communism compared to Marx's theory.

There are other differences though. The two I'll discuss here regarding this period are Lenin's concept of a revolutionary vanguard, as well as the dictatorship of the proletariat. The first is an intentional split from Marxism. For Marx, the revolution was meant to be organic, a realization by workers that Capitalism must be fought against as to better humanity. Marx viewed the revolution as something which would occur among workers as a whole. Lenin, on the other hand, believed a vanguard of the revolution was necessary to ensure the revolution's success. Lenin fundamentally conceptualized revolution as requiring workers to" embrace primarily and chiefly people whose profession consists of revolutionary activity". For Lenin, these professional revolutionaries would be the ones to lead the revolution and direct its path as necessary. This more concentrated force of revolution, which Lenin applied with the Bolshevik party (whose membership was at least initially more stringent and smaller), represents a distinct split from Marx's concept of revolution.

Finally, the difference regarding the dictatorship of the proletariat, maybe the least intentional split from Marx. To Marx, the revolution would require a 'dictatorship of the proletariat, where the majority working class would lead the minority capitalists as society transitioned to true Communism. Lenin and the Bolsheviks did not differ theoretically from this concept. However, the minority nature of the working class in Russia, alongside continual war, famine, and political upheaval, continued to elongate the period of the dictatorship. This eventually cemented the dictatorship, in various ways, in the Bolshevik's rule of Russia, and as such, created a split from Marx.

There are other differences, and of course, many more if you were to look at other periods of the Soviet Union. These three are simply some of the most relevant when it comes to understanding how Lenin's concept of Communism, and the Bolsheviks as a whole, differed from Marx's concepts.

Sources Used:

- Lenin, Vladimir, The State and Revolution, Peking: Foreign Language Press, 1973.

- Lenin, Vladimir, What is to be done, trans. S.V. and Patricia Utechin, Oxford: ClarendonPress, 1963.

- Marx, Karl, Selected Works in One Volume, London: Lawrence and Wishart, 1968.

- Marx, Karl, The Communist Manifesto, Melbourne: Penguin Group, 2010.

- Lenin, Vladimir, Lenin’s Collected Works Vol 26: Meeting of the Central Committee of theR.S.D.L.P.(B)., Moscow: Progress Publishers, 1972.https://www.marxists.org/archive/lenin/works/1917/oct/10a.htm.

- Rosenberg, William. “Workers and Workers’ Control in the Russian Revolution.” HistoryWorkshop, no. 5 (1978): 89–97. http://www.jstor.org/stable/4288160.