Sure, but "communist state" is a technical historical term that is simply the shorthand tag for countries similar to and influenced by the USSR. It originates in propaganda about communism (or socialism) related to these countries, but otherwise has little to do with communism or socialism as ideological/economic systems.

The propaganda origin is two-fold. Russian propaganda used these terms to ingratiate itself both with the revolutionaries who fought against the Tsar, and with European workers' parties at the time, trying to create a positive association between communism/socialism and their regime. As the disaster of Lenin and Stalin's takeover of power and totalitarian control started to become clearer after the war, the terms started being used by European and American propaganda machines to create a negative association between the Russian disaster and communism/socialism.

The fact that this was used for propaganda and did not reflect actual beliefs about the working of these systems is visible in the way the USSR's claims about being a democracy were never taken seriously, while its claims of being socialist/communist are presented as unassailable.

To be clear, socialism has a very simple definition - "workers' control of the means of production", or, in more modern terms, "democratic organization of the workplace". Basically an economic system is socialist if most/all enterprises are worker-owned co-ops, in contrast with a capitalist system, where most/all enterprises are owned by those with capital. The USSR and most other communist countries were totalitarian regimes where those in power exerted control over all enterprises, with workers at the bottom of the hierarchy, having even less say about the direction of their work than they do in capitalist systems.

Communism as an ideological term refers to a more extreme form of socialism, where not only do workers have control of their own work, but resources are actually pooled and the entire community has a say in the direction of each enterprise, including those that don't directly work in that enterprise. It is a far more idealistic model than socialism.

It's important to also note that socialism can easily happen in a free-market system, except that labor and enterprises can't be bought and sold - only goods and services. Communism is less compatible with the idea of a market, as it implies much more direct cooperation between stakeholders.