Communism is changing the state of things entirely, not merely changing or redistributing as your conception says - what you describe is closer to social democratic welfare state which is still fully capitalist.

The world is complicated, when it comes to economics you can go into the minutia all day and night but to summarize what communism actually is and how it differs from capitalism in simple terms, it'd be:

• The transformation of the mode of production. Instead of right now where you produce commodities to be sold on the market and that essentially dictating what to produce, goods would be specifically produced to fulfill needs, basically what is socially necessary for a society and its people to thrive, and all this would be coordinated via economic planning. The current system is incredibly inefficient, we overproduce a lot, workers can't physically buy all the goods on the market leading to waste or companies competing with its own unsold goods which decreases profit and leads to crisis where industry no longer becomes profitable, leading to unemployment. No more profit, no more things to buy, just make what people need.

• The abolition of money and private property. Not to be confused with personal property such as your home or car or toothbrush, access to wealth accumulation and private ownership of factories or land inevitably leads to monopolization, exploitation of labor (with factory ownership) or just parasitism where a person contributes nothing to a labor process, yet has the full right to everything produced by said labor.

• Kind of implicit in previous point, but abolition of classes entirely. If there's no way to privately own means of production or land, or accumulate a mountain of money that you can invest to get another mountain of money and snowball to oblivion, that would eliminate the aforementioned capitalists, landowners - no person would be superior to another due to their economic caste. Of course, a level of hierarchy would remain like foremen managing workers, but economically they'd be in the same position of having their needs met.

Hopefully that makes it easier to conceptualize that a different kind of system can theoretically exist that isn't capitalism - after all, we went from antiquity to feudalism to capitalism, all production modes of whom are drastically different, so why not communism?

Granted, we're yet to have communism given how it must be global, or at least on a very large scale. Capitalism itself is a global system, it relies on global trade and countries that decide not to participate (e.g. go autarky) suffer heavily, and communism which is primarily a "meet the needs" type of system cannot interact with global capitalist trade given how it produces and values goods in a much different way. Also, a single country cannot really have access to all the necessary resources to meet the needs with, so global cooperation is required, and this cooperation would ensure safety too given how prone Capitalism is towards imperialist wars.

As for other questions like "how would government look like" and stuff - that's mostly relevant for the transition towards it post-revolution given how this kind of society is simply unachievable in a capitalist dictatorships, liberal or otherwise, that we have today. While communism and its ideas are quite frankly weakest that they've ever been in terms of support, there's still multiple parties around the world, each having a different plan for the government.

Sorry for the wall of text, and do keep in mind that this is an oversimplification. Transition towards communism is equally as important, but I didn't want to go full hog explaining it given how it'd make it even more unreadable.