Nazism is not Fascist, as there are clear differences between Italian Fascism, Spanish Fascism and Nazism. As for 'left' and 'right' scales, they are useless for anything but populist media debates. Authoritarian scales are better, but they don't allow the media to divide society into two camps.
Nazism is an example of fascism. You are right that there are minor differences between different examples of fascism.
One of the strange things on this thread is posters lining up to change the meaning of the word 'fascism' so that it fits their prejudices mor comfortably, but unable to explan where they would then place Antonescu, Stroessner or Franco on a political map.
There are good reasons why Hitler is considered right wing, and one of them is the clear links between fascism and strong right-wing administrations like those of Pinochet.