Well I'd say communism is a type of socialism, where the latter is the ideal to strive for a better society for everyone, to intervene to help those who cannot help themselves.
Communism tries to achieve this goal by making the means of production into communal ownership. With the State enforcing strict wealth equality.
But it's still socialism with economic inequality at the beginning but fair and strong wealth redistribution in the end: equity.
Ah, communism is like unicorns. Many people like them but nobody have seen them alive. Because every communist state is not communist but authoritarian.
When does a Communist country become authoritarian? This line is always repeated by sympathetic liberals that haven't read theory yet think they know enough to judge Leftist movements.