What is an intrafaith conversation and how is it different from an interfaith one?

The simplest way to explain it is that the prefix matters.

Inter means between, among, in the midst of, mutually, reciprocally, together.
So interfaith is different religions being together.

On the other hand, intra means  within, inside, on the inside.
Intrafaith is one religion examining just itself in light of its interfaith experience.

We need both!

Graduate Theological Union professor Judith Berling explains it as two poles of interreligious learning:
1) understanding another religion faithfully, and
2) reappropriating Christian tradition in light of new understandings and relationships.

John S. Dunne, in The Way of All the Earth calls is the spiritual adventure of our time:

“What seems to be occurring is a phenomenon we might call ‘passing over,’ passing from one culture to another, from one way of life to another, from one religion to another.

“Passing over is a shifting of standpoint, a going over to the standpoint of another culture, another way of life, another religion (interfaith -italics mine).

“It is followed by an equal and opposite process we might call ‘coming back,’ coming back with new insight to one’s own culture, one’s own way of life, one’s own religion. . . (intrafaith)

“Passing over and coming back, it seems, is the spiritual adventure of our time.”