The inner one has to do with (via usual metaphor, "the war against oneself") - becoming ~wise/enlightened. The outer - with pedestrian wars n' stuff. The second is meant to be instituted only via post-graduates of the former.
In essence a most 'wise' distinction IMhO - but that doesn't stop those who flunked the inner work from ignoring their own holybook - and behaving quite homo-sappish, in God's Name (natch).
(This general idea, across all beliefs - as well as claimed un- non- or anti- such named classes)
As to conversion - as it is ever an emotional response to an 'epiphany' - why would we imagine that the methods of logical debate would have much more than slight relevance?
A.