How and why have socialists been historically divided over the means of achieving their goals?

Disagreement within socialism regarding means can be broadly divided into three disputes. First, the revolutionary strand, in the context of absent or limited suffrage, saw the fundamental restructuring of society via proletarian revolution as the only feasible or accessible route to change. By contrast, the evolutionary strand, emerging as the franchise was extending to include the working classes, at the same time as their wages and living standards within capitalism were rising, saw the urgency of dramatic political upheaval alleviated with the opening of a parliamentary, reformist path to socialism. Second, Marxists, seeing capitalism as necessarily and systematically exploitative in its quest for profit, advocate that the mode of production must be abolished and replaced. However, social democrats believe capitalism is redeemable and reconcilable with socialist goals; it can be 'humanized' through economic management and welfare provisions to reduce inequality. Third, disagreement is evident between orthodox Marxists and Communists. Whilst the former envision revolution as spontaneous and self-guided by a 'class-conscious' proletariat, the latter called upon the need for a vanguard party to lead the working class out of bourgeois delusion and towards emancipation.
It is important still to recognize that, despite these disagreements, socialists have been united by a commitment to the working class being the vehicle through which socialism can and should be achieved, and by a common belief in the necessity of changing capitalism as we know it.