Question:
What is the gift of faith (1 Corinthians 12:9)? Is it the faith that saves, or is it the supernatural faith that moves mountains?

Answer:
The context in which this verse is found is teaching us how the Spirit of God distributes spiritual gifts to members of the body of Christ. They are already saved, thus they do not need “the faith that saves.” Also, it is clear that though every member of the body of Christ receives a gift (vs. 7, 11), not all receive the same gift (vs. 8-10), so that the faith mentioned here could not be “the faith that saves,” for the “faith” in question here is limited to certain individuals.

I believe it is, as you said, “the supernatural faith that moves mountains.” One has said, “the gift of faith is the divine ability to remove mountains of difficulty in pursuing the will of God” (1 Corinthians 13:2), and to do great exploits for God in response to some command or promise of God as found in His Word or as communicated privately. George Muller is a classic example of a man with the gift of faith. Without ever making his needs known to anyone but God, he cared for 10,000 orphans over a period of sixty years.