What you believe matters as much, if not more, than the idea of faith itself. If not, truth has no relevancy in faith. To believe a lie and act on it, no matter how genuine the belief, might be thought of as being done "in faith," but it is not a faith that leads to salvation.
"Examine yourselves as to whether you are in the faith. Test yourselves. Do you not know yourselves, that Jesus Christ is in you?—unless indeed you are disqualified.” (2 Corinthians 13:5, NKJV)