Nihilism, in the sense of not believing in God, any purpose of life, any absolute truth, or life after death; is a subset of Atheism: all Nihilists are atheists; but not all Atheists are necessarily Nihilists.
Nihilism is common to a sub-group of atheists, rather than atheists as a whole. it is more typically associated with strong atheists (who believe there is no god) than weak atheists (who lack belief in a god). There may well be a relationship between Nihilism and 'Scientism' in which all aspects of existence, including our morality, society, etc are treated as something we can understand 'scientifically' and must therefore reject 'pre-scientific' concepts such as those that come from religion.But scientism is unusal because it establishes the possibility of deriving new objective truths and values from the world rather than being completely meaningless.
In the 19th century Nihilism was a movement in which people criticised existing ideas as illusions and rejecting what they didn't think was rational. This was originally part of the enlightenment tradition of philosophical scepticism and free thought but was taken to the absurd extreme of using reason to deny the rationality and existence of objective meaning. Consequently, nihilism is a self-contradictory and paradoxical belief that whilst all things lack meaning, we should still pursue rationalism to its logical conclusion that everything is subjective. it gained this negative assocation because of the terroristic and revolutionary movement in Russia in the 1860's, where political nihilism meant the rejection of all social institutions as irrational. The most significant work of this was
Catchetism of a Revolutionary (1869) by Sergy Nechayev. To give you an idea of how it reads, here's the first four lines.
1. The revolutionary is a doomed man. He has no personal interests, no business affairs, no emotions, no attachments, no property, and no name. Everything in him is wholly absorbed in the single thought and the single passion for revolution.
2. The revolutionary knows that in the very depths of his being, not only in words but also in deeds, he has broken all the bonds which tie him to the social order and the civilized world with all its laws, moralities, and customs, and with all its generally accepted conventions. He is their implacable enemy, and if he continues to live with them it is only in order to destroy them more speedily.
3. The revolutionary despises all doctrines and refuses to accept the mundane sciences, leaving them for future generations. He knows only one science: the science of destruction. For this reason, but only for this reason, he will study mechanics, physics, chemistry, and perhaps medicine. But all day and all night he studies the vital science of human beings, their characteristics and circumstances, and all the phenomena of the present social order. The object is perpetually the same: the surest and quickest way of destroying the whole filthy order.
4. The revolutionary despises public opinion. He despises and hates the existing social morality in all its manifestations. For him, morality is everything which contributes to the triumph of the revolution. Immoral and criminal is everything that stands in its way.
Nechayev is remarkable in the extremism of his words, but also that he did actually put it into practice. He killed one of the students in his own organisation and was senteced to prison for it. He eneded up in the Peter-Paul fortress in St. Petersberg, the highest security prison in Russian empire, and was able to establish a revolutionary organisation
within the prison by converting some of the prison guards to his cause by sheer force of personality and conviction. As political nihilism was essentially anarchist, he was freinds with the anarchist revolutionary Mikhail Bukunin who later rejected him as too extreme because Nechayev wanted to apply the standards of "revolutionary terror" not simply to the enemies of revolution, but also to its own ranks.
The Russian Nihilist movement may well have had an influence on Lenin and the Bolshevisks, and then later on the Communist movement (including Stalin, Mao, etc.) , but it is hotly debated precisely because the associations with nihilism are so toxic. additionally, nihilism is not a doctorine of
complete meaninglessness but as Nechayev put it, that a person should be "wholly asorbed in the sinlge thought and single passion for revolution"- so it's not
absolutely "meaningless", but is a very different definition of meaning to the one we are familar with in a judeao-christian understanding of objective truth and morality. it is more likely that communists reached similar conclusions due to their own ideas but it is an intresting and disturbing parallel to draw from the historians point of view.
Nihilism is therefore often associated with extreme destructive behaviours based on this tyrannical application of reason. it is possible to argue that nihilism, far from being the product of atheism, is in fact the product of religion in that our belief in reason acts as a form of god to which we must sacrifice ourselves or are so oppressed that we wage war against the world in an act of destruction and self-destruction . This is what Fredrich Nietzsche argued (himself more of an anti-nihilist) who said that the "death of god" necessitated a "transvaluation of all values" derived from god. He was referring specifically to Christianity, and described himself as
The Anti-Christ in rejecting christianity's perversion of what he saw as Jesus's true teaching: don't follow the Christ, become Christ.
However, it is both possible to have a belief in truth, meaning and purpose without the existence of god. The key is accepting that our belief in god and the sense of self are not identical, so that the destruction of religious faith is not the destruction of the self. The "soul" may not exist as a spiritual substance, but certainly the origin of the concept is related to our own subjective experience and our 'inner world' which can continue to have meaning even whilst we may strip it of supernatural attributes. Nihilism is however a major problem, particuarly in relation to Post-Modernism in which 'truth' is considered a social construct, and was itself influenced by a selective reading of Fredrich Nietzsches ideas.