I've spent a lifetime trying to figure it out and I have never succeeded. All I can tell you is that I reject the common American conservative assertion that National Socialism and Fascism must be leftwing because they are socialist or collectivist or promote big government. After all, patriotism and national identity are collectivist. I also reject the American conservative political spectrum which insists anarchists are on the right and totalitarians on the left because there are anarchists on the left (who prefer leftist totalitarians to rightist anarchists) and totalitarians on the right (who for some inexplicable reason are heroes to rightwing anarchists who hate leftwing anarchists). Furthermore, once one has dismissed Hitler (mach shemo!) and Mussolini one still has to deal with "big government" dictators like Francisco Franco, Antonio de Oliveira Salazar, Getulio Vargas, George Papadopoulos, Rafael Trujillo, etc., from whom many American conservatives have either supported or have never felt it necessary to distance themselves from. Have many American conservatives have ever claimed that Franco was on the left?
Then there is the unhappy fact that "fascism is on the right" is not an invention of the left. Fascist and national socialist movements themselves not only consider themselves rightwingers but as basically the only true anti-Communists just as Communists consider themselves the only true anti-Fascists. Back during the heyday of European fascism, fascist movements were hailed by many anti-Communists, not only in the United States, but among Zionists in 'Eretz Yisra'el (eg, ultra-right Zionist 'Abba' 'Achime'ir insisted that Hitler's [mach shemo!] anti-Semitism was merely a false outer garment to be rejected but that the essential nature of Nazism was anti-Communism and was to be embraced). So even as a conservative myself I find it somewhat facetious and dishonest for contemporary American rightwingers to suddenly discover that Communism and Fascism are the same thing because they both practice "big government."
The closest I have been able to come in determining the real difference between left and right (at least in their collectivist forms) is that the collectivism of the left is atomistic, egalitarian, and horizontal while that of the right is "organic," hierarchical, and vertical. But then there's the fact that many leftist "national liberation movements" (such as Kwame Nkrumah's in Ghana) supported by the Communist bloc (and other such movements supported by the contemporary left) actually seem to fit the definition of rightwing, rather than leftwing, collectivism. For some reason the only "non-western" peoples whose extreme nationalism seems to have a "rightwing" reputation are Japan and Turkey. Go fig.
I suppose ultimately it simply comes down to convention, and what one and one's enemies choose to label one.
The terms are a mess ... largely because they have been ripped out of context. They originally referred to the seating arrangements in a French parliament ... the revolutionary socialists on the left and the aristocratic traditionalists on the right. Any other use of the terms is metaphoric at best and obfuscatory at worst.
You bring up, for example, German National Socialism. And make no mistake, they truly were socialists ... Hitler read and was inspired by Marx. But they were also anticommunist. (IMO, that's because bloody totalitarian dictators don't like competition.) So: Does their socialism make them leftwing, or their anticommunism make them rightwing? Or are the terms nonsense?
If you haven't read any of Erik Von Kuehnelt-Leddihin's books, I strongly recommend them. Leftism is a great introductory history of socialist totalitarianism.
Incidentally, I more or less came to the point of rejecting the use of the terms generally, by way of rejecting them in the context of the Catholic Church after Vatican II. They're utterly inadequate to describe the polarization in that religious context, but they're also inadequate to describe American (or any other) politics.
Is the pro abortionist who also hates gun control Left, or Right? How about the welfare state advocate, who also supports a strong national defense?
Left and Right don't adequately describe either of them. But everybody has his own vague idea of what sort of political position the terms denote ... and those ideas aren't necessarily coherent from person to another.
contemporary American rightwingers to suddenly discover that Communism and Fascism are the same thing
I didn't "suddenly" discover that ... I realized it right away, 'way back in middle-school, when I learned what Communism and National Socialism were.
Have many American conservatives have ever claimed that Franco was on the left?
More of the problem: Do Left and Right describe economic freedom, personal freedom, religious freedom, something else? The original meaning (back to the French parliament) was economic.