Let's start with simple definitions. Dictionary.com has the following to say about believing vs. knowing:
Believe: to have confidence in the truth, the existence, or the reliability of something, although without absolute proof that one is right in doing so.
Know: to perceive or understand as fact or truth; to apprehend clearly and with certainty.These terms sound pretty similar to me. The only difference is that Believing in something involves a lack of "absolute proof", while knowing may or may not be based on such proof.
So that means the difference must be in "He can" vs "He will", right?
Well, not if you count the account of Meshach, Shadrach, and Abednego in the fiery furnace as a story of real faith. Remember, after all, they told Nebuchadnezzar that "our God whom we serve is able to deliver us from the burning fiery furnace, and he will deliver us out of your hand, O king" (Dan 3:17). This seems to fit the idea in the image above, but not if you look at the following verse: "But if not, be it known to you, O king, that we will not serve your gods or worship the golden image that you have set up" (Dan 3:18). In other words, we believe He is able and He will save us, but we acknowledge that He may choose not to.
And they stepped into the fire.
Because even if God did not act in the way that they hoped He would, the way they believed He could, they still had faith that His way is the best way, and they still would rather die in flames than bow down before a false god.
If that's not faith, I don't know what is.