In German, there are no two terms for those, both are called "Hakenkreuz". And the Nazi ideology actually made references to eastern culture and peoples, claiming that Germans were descendents of the Aryan peoples: https://encyclopedia.ushmm.org/content/en/article/aryan-1
And while Nazi antisemitism was of course descended from the traditional christian antisemitism, there were also parts of the Nazi movement that called for a replacement of christianity by an "Aryan" or "German" religion, which seems to have been a mixture of Germanic/Norse religion and more modern esotericisms.
So yes, while eastern religions are blameless for what the Nazis made of their symbol, it also isn't of christian descent either.
And while Nazi antisemitism was of course descended from the traditional christian antisemitism, there were also parts of the Nazi movement that called for a replacement of christianity by an "Aryan" or "German" religion, which seems to have been a mixture of Germanic/Norse religion and more modern esotericisms.
So yes, while eastern religions are blameless for what the Nazis made of their symbol, it also isn't of christian descent either.