Sounds like a biased question but I'll give a try anyway.

During the First International, various wildly different currents of socialism cohexisted in a not so peaceful way. Anarchists, communists, mazzinians, etc.

Bakunin said about Marx

As far as learning was concerned, Marx was, and is still, mored advanced than I... He called me a sentimental idealist, and he was right; I called him vain, perfidious and cunning, and I was right too

The main differences between anarchists and communists is not in their goals, but in the means to achieve them: anarchism lacks of dialectical materialism, analysis of socioeconomic relationships between classes and so on, which are what constitute the properly called Marxism. In this sense, Marxism is the scientific socialism, as opposed to the utopian one. Marx theorized the need of a transition phase to reach communism, which would be the "proletarian dictatorship". Bakunin and other anarchists completely refused this "transition phase" because, in Michail's words

• I hate Communism because it is the negation of liberty and because humanity is for me unthinkable without liberty. I am not a Communist, because Communism concentrates and swallows up in itself for the benefit of the State all the forces of society, because it inevitably leads to the concentration of property in the hands of the State, whereas I want the abolition of the State, the final eradication of the principle of authority and the patronage proper to the State, which under the pretext of moralizing and civilizing men has hitherto only enslaved, persecuted, exploited and corrupted them. I want to see society and collective or social property organized from below upwards, by way of free association, not from above downwards, by means of any kind of authority whatsoever.*

So, Bakunin wanted to achieve the max conceivable freedom immediately, overnight, so to say. Marx thought that this was (and is) impossible, because (among other reasons) not all countries on Earth are at the same social and economic level of development: Marx was sure that the proletarian revolution could be possible only in industrially advanced societies (=Germany, France, UK), with a strong bourgeoisie who had already a good level of "democracy". In other words, he was sure that a communist revolution was impossible in agricultural, backwards, ignorant Russia.

Thank you for your long and thought out response. No bias really -- just confused on Marx's ideas concerning a classless society free from hierarchy. It seems that human nature inevitably leads to greed and self interest. The end goal of Communism seems like a pipe dream; however, I will admit I'm not the most well read on Marxist theory. I was curious how exactly his ideas of a classless society differed from the utopian socialists. I understand he was a scientific socialist. Maybe I just need to figure out the difference between the two.