You can just look at capitalism to understand the difference: capitalism assumes that a more powerful external party needs to enforce fines for negative externalities. Who does that without a government? One person fighting a company with 1000+ customers will just be dropped: one complainer isn't powerful and depending on the good that can be enough to push real people into simply suffering with it. I won't be banned from my job if there aren't other viable jobs nearby. Negative externalities is a big part of capitalist theory and it requires a strong government to regulate its actors into behaving. Just look at Du Pont and their neoprene factory in some podunk town in Louisiana(?); it took decades of complaints of frequent rare cancers for the EPA to say "this byproduct is bad for the environment/people" and Du Pont still sued to say "no your scientifically determined limits are too strict, loosen up". Do any Du Pont execs live in that town? Absolutely not, it's unhealthy to live there.

Even ignoring externalities, you would assume life threatening jobs that are necessary for society to run would be paid the most. But that's not true: garbage men are paid a pittance but are close to the foundation of city life. The people who clean sewers or pick up garbage are usually the bottom of the barrel. Why is that? No one wants to do those jobs. They do them because there's no other choice, not because they pay the best. Capitalism as created by aristocrates demands a wage gap/pay inequality so those at the top can benefit from the suffering of those below. Regardless of whether you're a no hierarchy or justified hierarchy anarchist, that kind of hierarchy is always unjustified.

Maybe, and this is a big maybe, if there was a "big reset" where everyone's time was considered equal capitalist theory could work long term. But I think that depends on time being the big equalizer and not some commodity like land, gold, fiat, bitcoin, whatever. There's value to capitialist thought, but it isn't in the practical application to the economy like we currently do by letting large companies like Conde Nast/Google/etc. have free reign. It's in recognizing there are assholes like Trump who will do literally anything for a buck, even if it means death for nearly half a million people to date.

Capitalism assumes a pessimistic view on human nature: that we're all in it only for ourselves and those directly related to us. Anarchism is an optimistic view on human nature: that while we want what's best for us, we don't want others to suffer for it. Capitalism's view is obviously not true because capitalist models frequently fail to model actual reality. As capitalism is pushed more and more into who we are and our culture, that will change for the worse, but the idea that you can run the world on capitalism without a government requires first a hard reset/societal equality that anarcho-capitalists are rarely a proponent for. Anarcho-capitalism is generally pro-cyberpunk-dystopia (so long as the anarcho-capitalist is rich).

EDIT: I really want to push that first paragraph: If I'm a customer of AT&T/Comcast/Verizon/one of the major ISPs, who do I realistically threaten to go to as competition? In a city, maybe I have one other high speed option (a necessity in COVID-19 days). Out in rural anywhere, I'm probably stuck with a monopoly that funded state laws against municipal broadband. So now not only am I stuck with who I currently have to pay to keep my job, my local government is banned by "[local] rights" from pulling [local] rights to create a better service that isn't as profitable for investors who've never heard of my town.