It's not about the the end goal, it's about the way of achieving it. Anarchists and Marxists have praxis that often is mutually exclusive.

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.

You actually got me realizing that they're not exactly the same goal.

I'd normally say they are the same goal. If we're talking about marxist communism and anarcho-communism (I'd say by far the most popular flavor of anarchist ideology), the former seeks "a classless, stateless society" while the latter seeks "an end to all power hierarchy" and it's normally assumed that marxism's classless-stateless-society qualifies for the anarchist goal too because it's done away with two huge hierarchies: Class and state. But as any good anarchist can confirm for you, there are far more hierarchies than just class and state.

Perhaps marxists assume that class and state are the two threads that will in turn tug and undo all of society's other hierarchies. As an anarchist myself though... I certainly do not think that would happen. Hierarchy entrenches itself everywhere, and it would continue to do so after the end of states. The struggle would not be complete.

So to answer you question? I guess marxism seeks an end to two specific target hierarchies. Anarchism seeks and end to all of them. Perhaps they both seek and end to all of them, depending on the comrade you ask, but anarchism makes that explicit.

Figured I'd answer as a Marxist-Leninist that used to be an anarchist. Marxists and anarchists have similar, but distinct visions of what future society will eventually look like:

Anarchism is primarily about communalization of production. Marxism is primary about collectivization of production.

When I say "communalization," I mean anarchists propose horizontalist, decentralized cells, similar to early humanity's cooperative production but with more interconnection and modern tech. When I say collectivization, I mean the unification of all of humanity into one system, where production and distribution is planned collectively to satisfy the needs of everyone as best as possible.

For anarchists, collectivized society still seems to retain the state, as some anarchists conflate administration with the state as it represents a hierarchy. For Marxists, this focus on communalism creates inter-cell class distinctions, as each cell only truly owns their own means of production, giving rise to class distinctions and thus states in the future.

For Marxists, socialism must have a state, a state can only wither with respect to how far along it has come in collectivizing production and therefore eliminating class. All states are authoritarian, but we cannot get rid of the state without erasing the foundations of the state: class society, and to do so we must collectivize production and distribution globally. Socialist states, where the working class wields its authority against capitalists and fascists, are the means by which this collectivization can actually happen, and are fully in-line with Marx's beliefs. Communism as a stateless, classless, moneyless society is only possible post-socialism.

Anarchists obviously disagree with this, and see the state more as independent of class society and thus itself must be abolished outright.

Hope that was okay to post here!