Hang on - I said that if they were based on one or the other, they should be different. What you seem to be implicitly saying here (though I realize you explicitly disagreed with it earlier) is that religion isn't really based on mystical experience, but instead mystical experiences are attributed to the religion that the people experiencing them are already familiar with.No specific theology (which, for purposes of this discussion, includes animism), but belief in some sort of spirit world (which also includes animism).
The trance state itself commonly conveys a sense of presence, the rest is interpretation. Could be the spirit of the stag, could be Allah, and it mostly depends on cultural bias.
But you were the one who said the two would differ, so I return the question to you.