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This is a good summary. To simplify/describe it slightly differently, the definitions of capitalism and communism and socialism decribe the relationships between workers and the value of the work that they do.
Under capitalism, owners own the business and employ workers who are paid wages. The value of the products or services that the workers make is more than they are paid - and this extra value produced (profit) goes back to the owner. Thus, you end up with two classes of people, the workers/wage laborers (proletariat in communist jargon), and the owners (bourgeoisie in communist jargon).
In socialism, the workers own the businesses, and so the profit goes back to them instead of to the non-working owners. Thus in socialism, there is only the one class, the workers, and the bourgeoisie class has been removed.
This is extremely simplified, but I think describes the overall work and value relationships under the two systems.
I hope this helps too.
https://teachmecommunism.podbean.com/
https://revolutionaryleftradio.libsyn.com/
I really like these two podcasts for breaking down concepts, history, and significant figures. The second one has two spinoffs, Red Menace for individual works of theory and Guerilla History for historical events, which are both also great.
Start with reading Wikipedia articles.
This won't answer all your questions, but it will give you paths to investigate.
Some articles will be written as if you already know the subject matter, but they should give you enough stuff to keep digging.
This won't give you a degree in any of this, but it will give you plenty of puzzle pieces to build on as you see fit.
Read Socialism: Utopian and Scientific by Friedrich Engels. The quickest way to actually understand Capitalism is to work toward reading Marx's Capital with a group and other references. It might take a while to get there but this book by Engels will lay the groundwork for you to learn historical materialism and dialectical reasoning.
For Communism, read principles of Communism and the communist manifesto. But start with Socialism: Utopian & Scientific. Since communism hasn't ever existed, there have been communist groups and parties who may or may not have established different variations of socialism, there's nothing to study. You can study the history of communist parties and experiments, but there is a lot and much of it is sad or disappointing. Definitely learn about it, but its not where you should start.
Communism is a moneyless, stateless, classless society. Its a movement, something to work toward. It is not a system where the government owns everything. It isn't "authoritarianism". Its the opposite of those things.
