I quite like this summary from https://www.skeptic.ca/Anarchism_Introduction.htm because it points out a few key differences.

The basic tenet of anarchism is that hierarchical authority – be it state, church, patriarchy or economic elite – is not only unnecessary, but is inherently detrimental to the maximization of human potential. Anarchists generally believe that human beings are capable of managing their own affairs on the basis of creativity, cooperation, and mutual respect. It is believed that power is inherently corruptive, and that authorities are inevitably more concerned with self-perpetuation and increasing their own power than they are with doing what is best for their constituents. This is equally true in Totalitarian and Communist states as it is in Democracies. Anarchists generally maintain that ethics are a personal matter and by definition must be based on concern for others and the well being of society as a whole, rather than upon laws imposed by a secular or religious authority (including revered laws such as the U.S. Constitution). Not unlike existentialist philosophers such as Jean Paul Sartre, most anarchist philosophies hold that individuals are responsible for their own behavior, life goals and ultimate purposes in life. The anarchist needs no one to tell him what he ought to do and how to create a meaningful life. Paternalistic authorities foster a dehumanized mindset in which people expect elites to make decisions for them and meet their needs, rather than thinking and acting for themselves. When an authority arrogates to itself the right to overrule the most fundamental personal moral decisions, such as what is worth killing or dying for (as in military conscription or abortion), human freedom is immeasurably diminished.

Anarchists acknowledge the connection between various forms of oppression – including sexism, racism, heterosexism, classism, and national chauvinism – and recognize the futility of focusing opposition on one form of injustice while others continue to exist. Anarchists believe that the means one uses to transform the world must be in accord with the ends that one hopes to achieve. While anarchists disagree about strategies and tactics, including the need for formal organizations and the use of violent action to overthrow existing oppressive institutions and injustice, most agree that the focus must not be on merely destroying the current order, but on fashioning new, more humane and more rational alternatives to take its place.

While many anarchists value cooperation, communalism and collectivism, anarchists reject both the plutocracies of capitalist states based exclusively on greed and envy and the totalitarianism of the existing and recently fallen communist, or more accurately Marxist-Leninist, states. The rift between anarchists and Marxists developed as early as the 1870s as anarchists perceived that the Marxists were perpetuating authoritarianism under a different name. Marxist-leninists groups have traditionally emphasized the need for a vanguard party and the dictatorship of the proletariat, ideas which are fundamentally opposed to the anarchist focus on anti-authoritarianism and maximum individual freedom. Although orthodox Marxism predicts that the state will “wither away” with time, we have repeatedly seen in communist regimes a consolidation of state power and its attendant repression and insistence on conformity. The same oppressive authoritarianism has emerged in capitalist democracies.

I just re-read your question btw, and realized I kind of answered the wrong question here, because the quotes focus on the differences in the means rather than in the end goal. But it’s still good context, because communism has so far never been able to move beyond the authoritarian stage, so you could reasonably argue that the actual end state of communism is an authoritarian state with a socialist economy, especially if they have to co-exist in competition and conflict with capitalist states. So the end goal of the state “withering away” is more or less impossible to achieve via communism while western hegemony exists.

Everyone here is an anarchist so I’d like to give my view as far as I understand Marx.

People have already talked about anarchist views here anyways.

“The working class cannot simply lay hold of the ready-made state machinery, and wield it for its own purposes.” Marx.

The condition where revolution occurs is when contradictions reach a breaking point, Marx thought the proletariat would become conscious of its collective exploitation and overthrow the capitalist system.

This is not a gradual reform but a revolutionary transformation, since the capitalist state and its institutions (law, police, army, religion, ideology) serve the interests of the bourgeoisie.

Contradictions being the concentration of wealth in fewer hands (bourgeoisie) and the growing exploitation and alienation of the proletariat.

Then theres the infamous Dictatorship of the Proletariat which I see misunderstood in memes a lot here.

After the revolution, Marx envisioned a transitional phase but this is not a dictatorship in the modern sense, but the political rule of the working class.

In this stage:

• The workers would abolish private property in the means of production.
• They would use the state to suppress the former ruling class.
• Production would be organized collectively and democratically.

The state would begin to “wither away” as class divisions disappeared.

Then we get to communism and humanity reaches a stage of freedom and self-realization beyond the struggle for survival.

In Marx’s view, true communism is a classless, stateless, and moneyless society characterized by common ownership of the means of production, cooperative labor, abolition of alienated work and full human development and creativity.

Also Marx did not think communism could be imposed artificially or “designed” by intellectuals. It had to emerge historically, through the self-emancipation of the working class as capitalism exhausted its potential.

“The emancipation of the working classes must be conquered by the working classes themselves.”

To me the bone of contention between most anarchists and Marxists is that dictatorship of the proletariat phase. In a way you could argue for that being an anarchic structure in the right historical setting (not ours). “The dictatorship of the proletariat” tends to become simply a dictatorship. Theres no good solution to avoid this.

The more vaguely you read Marx the more anarchic you can make him. And hey after all, ‘if a philosopher really has compromised, it is the job of his followers to use the inner core of his thought to illuminate his own superficial expressions of it’ -Marx.

Now Marxism has changed as the world has changed. Globalism firstly is the big issue.

“The need of a constantly expanding market for its products chases the bourgeoisie over the whole surface of the globe. It must nestle everywhere, settle everywhere, establish connections everywhere.”

Marx saw “globalism” as a structural feature of capitalism itself.

There is the historical problem of Marx. His key prediction failed, he expected the proletarian revolution to occur first in the most advanced capitalist countries (like Britain or Germany). Instead revolutions happened mainly in less industrialized societies (e.g., Russia, China).

Capitalism has proved more resilient than he thought.

Now theres this idea in modern Marxism that the world is a single capitalist system divided into:

• Core (wealthy industrial states)

• Semi-periphery (developing industrial countries)

• Periphery (poor, raw-material-exporting nations)

Capitalism survives by shifting exploitation globally — cheap labor in the periphery sustains profits in the core.

This is globalized class domination. Institutions like the IMF, World Bank, and WTO enforce capitalist rules worldwide. Outsourcing, financialization, and global supply chains reproduce class inequalities internationally.

Then theres the cosmopolitan Marxists, who think the working class must organize globally too. Problems like climate change, migration, and corporate power are transnational, so solutions must be as well. They advocate global labor solidarity, international regulation of capital, and a cosmopolitan socialism that builds institutions beyond the nation-state. This position differs from older Marxist anti-globalization movements, which often viewed globalism purely as imperialism.