There is an intense fight over what communism means but essentially the two are overlapping ideas. There are anarcho-communists like myself who think that there should be communal resource sharing under a system of personal unions (unions of people instead of states) and social commons. This is also sometimes called “libertarian communism” though libcoms are not necessarily anarchists.
This is obviously different from the Stalinist version of communism (which is itself changed from the roots of the movement) in which as strong state enforces complete control over the economy. So Stalinism is a kind of “authoritarian communism”.
Yet still there are many anarchists who are not necessarily communists, like mutualists, egoists, christian anarchists, queer anarchists, and green anarchists (ecological anarchists).
A Diagram:
About “People Pretending to be Anarchists”, these are what are called “entryist movements”. Their goal is to gain access and control over the spaces anarchists meet in and then to inject their ideas while bullying critical voices into silence.
At least two of these (”National Anarchism” and “Anarcho-fascism”) were invented by explicit fascists who wanted to draw in people at the fringes of the anarchist movement (who might not know better) and bring them into line with fascist goals (the goals of both are the same as the goals of the alt-right under Richard Spencer, the creation of a white-only “ethnostate”).
“Anarcho”-capitalism was started in the wake of Murray Rothbard having successfully led the “Libertarian capitalist” movement to seize the term “libertarian” to mean a certain brand of capitalists when it had referred specifically to libertarian communists since it was invented 120 years before.
The goal of “anarcho”-capitalism is to seize control of the term “anarchism” so that it refers to capitalists in the same way. Their ideas are indistinguishable from the Austrian School of economics, which is a particularly vicious capitalist ideology. In practice their best given example of an “anarcho”-capitalist hero is Augusto Pinochet, a brutal and murderous military dictator who seized control of Chile in a coup.
Agorism, afaik, split off of “anarcho”-capitalism and carries a lot of the ideas associated with national “anarchism”.