Trotsky believed that for Marxist revolution to succeed, it had to ignite similar movements globally. Stalin believed contrariwise. But then his main aim was not the emancipation of humanity from under the iron heel of capitalist imperialism but to win the power struggle as to who should be the heir to Marxism-Leninism and lead the Soviet Union. This he did so and then seeing that Trotsky would remain a danger to him had him exiled and then later assassinated in Mexico. It goes without saying that Marxism-Leninism should be distinguished from Stalinism, after all, it was Lenin himself that cautioned that Stalin required watching.
Similar sentiments to Trotsky were expressed by Rosa Luxembourg who then developed a theory which widened the site of conflict from the industrialised countries of the west to the more rural colonial possessions of the west in British India and French Indochina. This is one of the major successes of socialism, the decolonisation movement that swept the globe in the aftermath of the second world war. It's this revolutionary sense of socialism that probably motivated Cuba to intervene in Angola against the racist and capitalist regime of the then aparthied South Africa and prompted Che Guevara to go to Bolivia in an attempt to foment a revolution in Latin America.
Trotsky's view - that for socialism to win would require seeding, nurturing and battling for socialism in many countries - was imitated by the West who then realised to counter Trotsky's vision would require a counter strategy of capitalist imperial containment. Imitation, as Oscar Wilde said, is the sincerest form of flattery that mediocrity pays to greatness.
It's this that's commonly said that motivated the USA's aggressive and genocidal war in Vietnam. However, Ramsey Clark, attorney general during Johnson's administration and then later supreme court justice, went on a visit to Vietnam in 1972 during the height of the war and on the radio station, Voice of Vietnam, angrily condemned the American bombing raids, accusing them of bombing Vietnam "back to the 17th C" and purposefully targeting civilian areas. He later called his own government, echoing Martin Luthor King, "the greatest human rights violater in the world" and that it routinely bullies and mistreats poor, minority and politically powerless peoples. It's this critique that has been taken up post-colonial theorists - after all, both France and Italy had powerful communist parties - and neither were bombed by the US "back to the 17th C."