Disclaimer: I am very new at this - if I have broken a rule, inform me and I can delete this comment no problem.

The communist government system which was formed by Lenin was inspired heavily by Karl Marx, and his work The Communist Manifesto. Marx's followers essentially beleived that there was a heirarchy of government system - 'stages' - which went like so:

Communalism (think caveman) -> Slave society -> Feudalism -> Capitalism -> Socialism -> Communism.

Marxists beleived that the higher the stage, the more advance the society was, and the more power the people (working class) had. They also beleived in permanent revolution, in other words, that the working class would always be in a state of struggle against the ruling class until true communism was acheived. Finally, Marxists believed that this should be a global struggle for revolution, and that all societies will be in a state of revolution until true communism is acheived.

Lenin was a Marxist, and with the communist party he set up, he followed many of Marx's economic and governmental policies. For example, 'Comitern' was set up, who's mission statement is:

"to fight for the creation of an international Soviet republic as a transition stage to the complete abolition of the State."

Very similar to marxism, as it promotes these stages of revolution internationally, with an end goal of the working class being in power.

However, when Stalin came to power he immedialty introduced the idea of 'Socialism in one country'. He rejected the idea of 'the global struggle for revolution', deciding to instead focus on the national needs of the USSR itself (following the failure of the communist party in Britain and other countries). He also rejected the idea that eventually, his government system should be in the hands of the people (which is what Lenin hoped; Socialist democracy). He believed that a single-party ruling state would always be needed. These differing values can be seen in his ruthless takeover of the single party system via party purges, and his disdain and manipulation of any democratic system.

Finally, one can sum up the difference very crudely by saying that Lenin was idealistic, whereas Stalin was realistic and concerned with consolidating his power. Lenin very much set up his party in what he believed to be ideologically true, and conductive to revolution from below. On the other hand, Stalin more-or-less did was was neccessary to assure his own security and retain his power.

Edit: Also, my main source for all this is Allan Todd's and Sally Waller's Authoritarian and Single Party States Text book, although I can supply supplementary sources for something if you ask.