【Anarchy】 and 【anarchism】 overlap in their implications but are not synonyms because of differing denotations.
【Anarchy】 may denote a state or condition of society where there is no law or imposed order because social evolution has rendered these unnecessary.
first the proletarian revolution . . . then the dictatorship of the proletariat; and lastly, the classless society: that is the Marxian order of advance towards communism and 【anarchy】 , towards justice, equality and perfect freedom —Plamenatz
It may, on the other hand, denote one of complete disorder resulting from the breakdown of normal controls.
for our people liberty so often means only license and 【anarchy】 —Sulzberger
【Anarchism】 denotes a theory that government is an evil because it imposes limitations upon the freedom of the individual.
nihilism is a form of 【anarchism】
The same distinctions extend to their respective adjectives anarchic and anarchistic.
anarchic disorder
anarchic conditions
anarchistic influences
anarchistic doctrines
Anarchist when used adjectivally is often ambiguous since it is related to both 【anarchism】 and 【anarchy】 .
an anarchist plot to assassinate the prime minister