If we want to get technical about it, here's an explanation about the difference, and how and why it's done matters.
Before reading (if you can be bothered), remember, you're the one that got pedantic about it:
https://en.wikipedia.org/wiki/Nazi_salute
'The Nazi salute was not invented by Adolf Hitler or Benito Mussolini, nor is it limited in time to the Second World War or in place to Europe. The salute dates all the way back to the Roman Empire and is properly known as the Roman salute (Saluto Romano).
The Roman salute is made by thrusting the right arm forward, palm facing downwards, at an angle of around 45 degrees (Mussolini's version was a bit higher; Hitler's lower)'. Source 1. Lundmark T. Hi, Hitler! arm salutes at various angles. In: Tales of Hi and Bye: Greeting and Parting Rituals Around the World. Cambridge University Press; 2009:18-25.
https://www.ushmm.org/antisemitism/what-is-antisemitism/origins-of-neo-nazi-and-white-supremacist-terms-and-symbols