TL;DR:

Socialism: maintains monetary system. You earn and spend money like usual, except you are restricted from using the labor of others to generate profit for yourself (example: maintaining a large business). Key formula: from each according to their abilities, to each according to their labor.

Example of a socialist country: USSR, Eastern Bloc, Mao’s China, Castro’s Cuba, Allende’s Chile.

What socialism is not: Nordic model, capitalist states with social support.

Communism: no monetary system. Everything is free. Communism assumes one of three ways to make it happen: either everyone understands the intrinsic value of labor and does it for the sake of it, or labor is mandatory, or all of the unlikeable jobs are automated. Communism is normally considered not as an immediate outcome, but a future goal. Key formula: from each according to their ability, to each according to their needs

Example of a communist country: War communism period in Soviet Russia

What communism is not: socialism, capitalism with state support.