Fundamental difference in realms of impact - one is entirely temporal (political), one is fundamentally spiritual but tries to affect the temporal (religion).
Fwiw OP the interaction and separation of the political and religious sphere is one area that's been debated hotly by academics for centuries. I use the spiritual temporal divide as a parsimonious example because that was one of the first differences introduced to me in this discourse when I was an undergraduate. Of course these differences are not uniform, but if we're going to use 'Otherism' as the main benchmark for discussing whether an entity is 'religious' then we're going to be cast too great a net.
Fwiw OP the interaction and separation of the political and religious sphere is one area that's been debated hotly by academics for centuries. I use the spiritual temporal divide as a parsimonious example because that was one of the first differences introduced to me in this discourse when I was an undergraduate. Of course these differences are not uniform, but if we're going to use 'Otherism' as the main benchmark for discussing whether an entity is 'religious' then we're going to be cast too great a net.