I will add to it:
Both of these political systems were totalitarian systems : both were supposed to create a "perfect" state based on the values of each systems (which are more often than not fundamentally different). In both cases it is important to differentiate theory from how it was applied IRL : communism was implemented in different ways in different states, ditto for fascism.
Briefly, communism is an ideology that promotes an equalitarian, classless society in which the means of productions are owned by the collectivity. A theory that is meant for the common good, and with good intents, but that requires violent revolution nonetheless. Attempts at communism have generally led to totalitarian states, in which the state becomes all poweful, using all means in its power to "protect the revolution", and eventually to prevent itself from falling apart after a few years. Of course, most communism-inspired states are based on the Soviet Union, which wasn't exactly a success for the reasons we know, so we have very few examples of anarchist communism.
Fascism, unlike Communism, isn't a definite ideology in itself, but it can be used to describe modern dictatorships. Generally, fascism is an ultra-nationalistic trend, not always "tribal" in the national socialist sense of the word, but that clearly doesn't favor multiculturalism and universal tolerance. It generally encourages militarism, traditionalist politicies and religion, all the while showing great disdain for leftist organizations such as labor unions. Even then, fascist states tend to favor populist policies and state interventionism, unlike the economic right. Like soviet communism, fascism leads to all-powerful states that policy every aspects of one's life, and definitively doesn't favor any form of democracy.
Thus, we can say both communism and fascism produce totalitarian, all powerful states that are often very similar in practice, but their purposes and objectives are very different. Communism aims at creating an ultra-equalitarian society, while fascism favors a conservative, social darwinist one. It is a strange twist of irony that both are so different, yet somehow very similar.
