Two major strands of revolutionary socialism, hoping to achieve similar ends but by pretty different means.
In the conflict between Marx and Bakunin that defined the First International, at issue were both the method and goals of organizing the proletariat against the bourgeoisie.
In Marx’s view, it was necessary that there be a centralized leadership coordinating the struggle. Further, the goal of the struggle would be proletarian state ownership of the means of production. All this was incompatible, in Bakunin’s eyes, with the aims of the workers and would lead unavoidably to a new repressive political structure.
What Bakunin found onerous in Marx’s politics, both in its strategy and its goal, was the idea of representation as a political concept. Where there is representation, there is oppression. Anarchism can be defined as the struggle against representation in public life.