One of the dangers of reducing faith to just a belief in a fact is that we reduce our walk with God down to just a list of facts that don't really make much of a difference in our lives.
"But someone will say, "You have faith and I have works." Show me your faith apart from your works, and I will show you my faith by my works. You believe that God is one; you do well. Even the demons-and shudder!" James 2:18-19
The argument that James is countering is that you can have faith without having works of obedience. In other words, you can have faith that really doesn't affect your real life.
He says show me your faith apart from your works. Prove that you really have this faith. His point is that you can't.
Ultimately, true faith is more than just agreeing with a truth. It's more than just saying I believe that is accurate. That's why he goes on to say that even the demons believe the facts. They know who God is (they even shudder). They believe the facts of the gospel, but they aren't part of the kingdom of God. They don't have faith.
So what is faith?
Faith is a whole-hearted, surrendering, resting trust in God, His Word, and His works. Faith sees Christ as everything we need and leads us to abandon everything for Him. It leads us to trust Him wholly with our lives. It leads us to see Him as superior. It leads us to lovingly pursue Him each and every moment.
If you have this kind of faith, then James says it will be seen in your life. Your faith will be seen by the works in your life because if you have true faith in Christ, it will transform you in real ways.
The facts are important. We believe the facts, but if we don't surrender to the King we don't have anything. Saying you are a Christian means absolutely nothing if you don't belong to Jesus. Going to church doesn't make you anything if you don't rest your all in the Savior.
That's why faith makes all the difference. When we have that kind of faith, it changes everything about our lives. It means there is no area of our lives that isn't under the rule and reign of our awesome King! This is the place where we really come alive, when we live by faith. This is the place where our lives are filled with fruit that shines Christ each an every day, when we live by faith.