Question is somewhat difficult to answer. The primary similarity seems to point to an agreement on spontaneous revolt being a force of power (i.e. the behavior of revolutionary agency). From here there is disagreements.
Anarchists typically don't share the communist view of proletarian as the only social caste with this agency, but on the flip side, many communists see the proletariat as a description of an agency not exclusive to the working class. So the small businessman, the vagrant, the small criminal, the peasant, etc. are pulled with the working class when proletarian consciousness expands. This is being conscious of their social caste and its relationship to the social order + the will to destroy this relationship.
Anarchist syndicalism and its relationship to council communism is seen as similar, but this is largely a confused view because anarchist syndicalists participated with council communists in worker councils during periods of unrest and insurrection. Industrial unionism is mostly rejected by informed council communists while anarchist syndicalists often view being only for worker councils as a position of self marginalization. However, individuals may cross over rather frequently depending on how they like to practice being for revolution.
The left communism of Bordiga and those influenced by his thoughts show another behavior that anarchists can both agree and disagree with in many ways. Those "for revolution" (for the spreading of propaganda, in word and deed, in favor of revolution) can find much common ground, but usually in narrow ways.
Left communists typically reject the anarchist tactics of propaganda because they are considered too militant and lacking in strategy while anarchists typically reject left communist theoretic positions due to heavy semantic disagreements and often because the left communists still organize their political organizations as 'parties' or anarchists outright reject political organizations.
On the flip side council communists can often agree with this anarchist position and is often how council communists and left communists disagree. This does not mean anarchists can't work with left communist parties (because often they do), but it does mean anarchists usually don't join left communist parties.
Anarchists in favor of political organizations and/or industrial unionism often find themselves disagreeing with spontaneous agency, so they also often disagree with much of the above. Instead they build anarchist specific political organizations and various working class based institutions that can aid the working class reach a point where they can challenge and overcome the social order.
In later times, these lines are sometimes blurred. Autonomists can mix with anarchists and communists within action networks for example. Another would be propaganda organizations, like the Situationist International, where both communists and anarchists participated.
While this doesn't directly answer the question, authors and actors have shared influence on anarchists and communists generally along these lines of thought