Is there a term for a group believing their methods are better than another?

Solution 1:

The group within a group you are talking about sounds like a faction. Finding a word for one that thinks they have better ideas is likely to be impossible, since they all believe their ideas are better. Since they all believe they are better there was never any need to invent a term for them. Since I write scifi, that has never stopped me from inventing new terminology. How about "narcifaction" (narcissist + faction) or you could take the main idea of whatever your faction believes and put the word "faction" after it. Or you could just call them "the one true way" or something like that, which would be something they call themselves. Or, you could call them the "Those deceived" which everyone else would call them, or use a derogatory term made from their beliefs such as "flatworlder" for those who believe in a flat earth.