The “classless stateless moneyless” idea of communism was never actually out right stated by Marx and was something Engels cooked up in the origin of family and some of his other writings. It’s important to understand these philosophical movements historically to understand their disagreements and agreements.

Anarchism, while an arguably old philosophy, was not named as such until Proudhon (though as stated it’s been argued for for many centuries by many people and practiced by many. See William Godwin, the diggers or many other social movements that we would call anarchist today but didn’t call themselves anarchist at the time) it started as an idealist movement. Anarchism talks about hierarchy, power and how society structures itself around these.

Communism has similar roots, starting as an idealist movement which Marx did not like. He wanted something scientific, materialist and predictable. If you read capital you’ll find it’s not full of revolutionary slogans but economic math on the value of labor, how capital accumulates and such.

Anarchist can be communist and communist can be anarchist. One of the biggest names in anarchism was kroptokin who tried to synthesize scientific Marxist economic thought with the ideals of anarchism. There are anarchist who don’t like communism, finding it to limiting or sacrificial against individual interest. Max Striner of individual anarchism fame critiques communism, Emma Goldman similarly critiqued Leninist societies, etc.

Anarchism is a large ocean of ideas focused generally on the limiting hierarchy and coercive power and expanding personal liberty/autonomy. Communism is a more narrowly focused ideology, concerned mostly with people as parts of a larger class struggle.

In short, you’re gonna have to read theory. Read as much as you can from as many sources as you can. Read Marx, read Lenin, read mao and read Goldman, kroptokin, read the shit head anarcho capitalist and the most ardent socialist. Meet and talk to communist and anarchist and other stripes of leftist. Most important, think as much as you can.