Leninism is the blanket term for the analyses and strategies of anyone who finds political and strategic inspiration in the Bolshevik seizure of state power in Russia in October 1917.
Leninism is distinguished by the following characteristics: a semi-clandestine professionalized revolutionary party that seeks to infuse the industrial workers (and to a lesser extent depending on local circumstances, the peasantry and demobilized military -- hence the somewhat cumbersome Soviets of Workers, Peasants, and Soldiers) with revolutionary consciousness through agitation and propaganda (Lenin famously wrote that the working class by itself could only attain what he called "trade-union consciousness" and fight for bread and butter issues); the use (internal to the Party) of Democratic Centralism, whereby the leaders centrally decide policies for the rank and file, who are expected to carry out those policies; the external use of a Cheka (political police) to help consolidate and maintain political hegemony; the expropriation of industry and real estate and banks; the increased development of the Productive Forces in order to increase the size of the proletariat, which is understood to be the Revolutionary Subject, destined to become a "class for itself" and abolish capitalism (and according to some, the state as well). As a successful revolutionary movement, anyone who opposes them (whether from the left or right) is "objectively counter-revolutionary."
Trotskyists, Maoists, Stalinists, and the various other sub-sects of Marxists (who at some point will refer to the ideas and practices of Lenin) are all Leninists. The main distinctions (and even these are probably too detailed) are as follows:
Trotskyists see themselves as the authentic heirs to the revolutionary successes of the Bolsheviks in the period before the rise of Stalin in 1924. They are fans of what they call democracy (internal to the workers' movement) and frequently favor the policy of the United Front (a temporary defensive formation of [at least potentially] radical workers and their organizations, whether Leninist or not) against some greater enemy (whoever or whatever that might be). As a distinct political tendency, they are the most likely to split (the joke is about the 57 varieties), especially over what to those of us on the outside might think are really minor issues; no Leninist organization since 1921 tolerates internal dissent. Splits are named after the dude who put the new spin on material conditions (or whatever other arcane reason) that necessitated a new interpretation of Marxism. There are Marcyites, Shachtmanites, Pabloites, Lambertites, and who knows how many others? They are internationalists who recognize the oppression of nations that is the legacy of colonialism, but mostly refuse to support national liberation struggles, which are almost always cross-class alliances (Popular Fronts, see below). Exceptions are sometimes made for the sake of the development of the local Productive Forces, depending on the sect of Trotskyism. Trotskyists hate Stalinists, and the feeling is mutual. In relation to the former Soviet Union (and other Stalinist regimes), some Trots have a theory of the Deformed Workers' State, which posits that the expropriation of the Russian (and foreign) bourgeoisie in 1917 meant that the USSR had truly abolished capitalism, but that when the Stalinist bureaucracy came to prominence, the proletarian character of the state was then "deformed," and all subsequent states that sought to emulate Stalin's regime were likewise "deformed." But since they were authentic workers' states, they needed to be defended against the international bourgeoisie (and fascists of course) and their capitalist states. Most Trotskyists will run candidates for local elections; one of their old electoral formations is the Peace and Freedom Party. They refer to themselves as real Marxists or Trotskyists.
Stalinists are adherents to the highly centralized, authoritarian, and brutal policies of The Great Leader. Dissent among Stalinists can result in splits in the Party, but because Stalinists are even less tolerant than Trots, it is often accompanied by beatings, arrest, imprisonment, torture, and murder. The Revolutionary Subject remains the industrial proletariat. Stalinists continue to promote Popular Fronts, defensive formations made up of an alliance of self-described revolutionaries with allegedly progressive elements of the middle classes. Stalinists, as fans and promoters of Socialism in One Country, are nationalists, favoring just about any Popular Front with the potential to cause trouble for capitalism. They are the most socially regressive tendency on the Left, often writing off patriarchy, homophobia, and other forms of specific oppressions as characteristics of capitalism; once capitalism is destroyed, those problems are supposed to disappear since the material reasons for their existence will also have disappeared. Their primary targets for liquidation are Trotskyists (whom they refer to disparagingly as "Trotskyites") but anarchists and other independent proletarian revolutionaries are always on the hit list. They declare some sort of adherence to Democratic Centralism, but all decisions are always made through a strictly hierarchical bureaucracy. Needless to say, they fully supported every policy of the former Soviet Union despite the twists and turn and about-faces. Some Stalinists will run candidates in elections, but they almost never profess Stalinism, except in Europe, where "Eurocommunism" was the innovation. They often refer to themselves as Marxist-Leninists.
Maoism is Stalinism for the revolutionary peasantry; Mao altered the formulation of the Revolutionary Subject not just to include peasants, but as a replacement of the primacy of the industrial proletariat. Maoism gives us the Theory of the Three Worlds, especially after the famous Sino-Soviet split; Mao saw the post-Stalin USSR and all those who remained loyal to Moscow (the Second World) as the primary geopolitical threat to the existence of the PRC despite the continued ideological animosity of the First World (capitalist countries). All the characteristics of Stalinism are included in Maoism, from the support of nationalism of oppressed minorities to the formulation of identity politics. Splits among Maoists have to do with splits in the PRC in the mid-60s, with local cultural issues feeding into them. Some Maoists (like the RCP) are homophobic, while their Maoist enemies are into women's and gay liberation as befits the promotion of identity politics. They almost never engage in the electoral process. They call themselves Maoists.
The relevant common denominator for anarchists is authoritarianism.
