The difference is mostly in how they implemented it.
That’s literally true, but nowhere near enough to somehow transform fascism into anything right wing.
One would have to somehow accuse Lenin and Stalin of being “right wing” too in the vein the modern left uses, the former for his “New Economic Policy” and the latter for his “socialism in one country” (this latter being the inspiration for China’s “socialism with Chinese characteristics”; see how both imply the label “national socialism”).