The government interferes with the economy to influence our behavior, so economies are inherently tied to politics. Eg giving a tax break if you have a child, or applying tariffs to imported goods. Or even more broadly, globalization and colonialism.

The way each political party might interfere with each economic system and use it to regulate the people can be different as well. Theoretically, communism is anarchist in nature and moneyless, so the economic system would change the government, and the government would change the economic system.