Anyone who researches political science will understand (as you imply with the "or") that anarchism and communism are separate and distinct political philosophies.
However -- We all know that the Left likes to change the meaning of words (ex. "liberal" used to mean small government, today, "Liberal" means big government). I can tell you that in the 21st century, about 99% of the "anarchists" in the world support Big Government, Central Control with lots of restrictions on what is considered acceptable behavior, and taking from people according to their ability to produce, and giving to people according to their needs. Today -- contrary to long-standing historical meanings -- there is almost no practical difference between an "anarchist" and a communist.
Isn’t that concept from the Bible?
Acts 4:34-35
There was not a needy person among them, for as many as were owners of lands or houses sold them and brought the proceeds of what was sold and laid it at the apostles’ feet, and it was distributed to each as any had need.