In its day, fascism involved combat and suppression of Marxists and communists, but the opposition between fascism and communism has often been exaggerated. On the one hand, opposition to communism motivated many to support fascism in defense of property and private enterprise. On the other hand, Leninism was in many ways a model and precursor for fascism, as well as an opponent. Both sought total mobilization and control of society.
It's hard to imagine that fascism would have caught on as much as did without Marxism-Leninists as competitor, threat, precursor and example, but one can easily imagine societies divided along other lines, racial or ethnic or religious or cultural, that would adopt fascist policies. It's egocentrism that makes communists think that it's all about them.
Another important element behind historical fascism was the First World War. The vision of civil society as a battlefield, the hunger for redemption through violence, and the idea of mobilizing society for combat made their way into the bloodstream of the era, left and right.
Many Third World dictatorships in recent years have had much in common with fascism, but the intensity, the hunger for war and conquest, and the fear and desire for revolution weren't present. Fascism is "hot" and impassioned, while contemporary society tends to be "cool" and dispassionate.
But if you asked a fascist what his movement was about, he might well talk about the corporate state and representation by occupational groups, things that get left out of modern polemical definitions of fascism.
Fascism essentially is the goverment support of one group at the expense of another. Private property, controlled by the state. You use the property for government ends, you keep it. You don't you lose it.
Amerika is in the process of creating our own brand of Fascism today.