It might surprise some of you that I run into both supporters of fascism and people who terribly misunderstand fascism historically on a very regular basis. I see at least one or the other almost weekly; certainly almost every month for the past half decade.
You might say that it's simply because of Godwin's Law: Any vociferous argument over the internet will inevitably wind up with comparing people to Nazis. I don't really believe in Godwin's Law, but for a common touchstone, fascism certainly is poorly understood, and since fascists are almost shorthand for evil, well, it's easy to see the motives for the poorly stretched analogis to Godwin's Law.
And it's not limited to casual discussion on the internet. The political right has been working hard to cast Hitler as part and parcel of the political left, an exercise that reached new heights with Jonah Goldberg's book Liberal Fascism, and something truly remarkable to historians who recall that the architects of fascism explicitly identified liberals as a problem. The conflation of "socialist" with "national socialist" is one I have seen all too many times.
It's with good reason that historians put fascism on the right side of the political spectrum, but it would also be naive to confuse the modern political right with fascism. Modern fascists and - if you are one of those few who draws a distincition - neonazis almost always align themselves within the political right wing (e.g., David Duke), although the mainstream of the political right generally disowns their support. Historically, fascists drew their support from business elites, corporate interests, and traditionalists, core groups for conservative movements now.
There are common elements, such as the invocation of nationalist sentiment, militarism, leaning heavily on traditional family values, and getting "outsider" ethnic groups to conform to an identified traditional norm or leave; there are also critical differences, such as theoretical economic policy.
Right wing ideologues will at least claim to support the free market - fascism, however, was nearly as opposed to lassez faire economics as it was to socialism. Proponents described it as a "third way," neither communist nor free-market. To understand fascism - and I only suspect that I do - it is necessary to understand that fascism is all about the good of the nation. In the Nazi model, we insert the good of the race as a template over the good of the nation, but in both cases, it is about competition and strength. Social Darwinism is probably the most compelling ideological inspiration for fascism; and at its core, fascism is not particularly peaceful.
When conflict can serve to strengthen a nation, weeding out weaker elements within the nation and weaker nations within the world, conflict becomes desirable.
But everybody already knows what fascists are. Fascists are people who do and believe something different from you politically, who you think are forcing the wrong thing upon you... right? Leave alone this nonsense about "historical reality," you know what you want to believe!