The fact that it shows up in both noun and verb form does not alter its meaning. Both mean faith or belief. The very fact that pisteuo is a verb certifies that there is actionable behavior linked to pistis. Scripture never disonnects the acknowledgement of a set of facts from the behaviors that give legitimacy to what one believes to be true. James says that to do so is not faith. Both of these dynamics are inseparable.
James even offers the impossible challenge to prove his point. "If a man says he has faith, but he has no works? Can that faith save him? This is a rhetorical question to which the obvious answer is NO! The challenge is the offered to the one who would attempt to legitimize his faith without works. "You have faith, and I have works; show me your faith without the works, (This is an impossibility) and I will show you my faith by my works.” Thus, works legitimizes the claim of faith. These linking dynamics cannot be separated. This is precisely what the Hebrew writer demonstrates in chapter 11.
In James 2:21, notice closely that James does not say that Abraham's work of offering up Isaac resulted in God's accounting Abraham as righteous. The accounting of Abraham's faith as righteousness was made in Genesis 15:6, many years before his work of offering up Isaac recorded in Genesis 22. The work of Abraham did not have some kind of intrinsic merit to save his soul, but it proved or manifested the genuineness of his faith.
This is the sense in which Abraham was justified by works. He was "shown to be righteous." When Abraham performed the good work in Genesis 22; he fulfilled the expectations created by the pronouncement of his faith in Genesis 15:6. Abraham was accounted as righteous based on his faith (Genesis 15:6) not his works (Romans 4:2-3) long before he offered up Isaac on the altar and demonstrated the reality of his faith in Genesis 22.
Christ saves us through faith based on the merits of His finished work of redemption "alone" and not on the merits of our works. It is through faith "in Christ alone" (and not by the merits of our works) that we are justified on account of Christ (Romans 3:24; 5:1; 5:9); yet the faith that justifies is never alone (solitary, unfruitful, barren) if it is genuine (James 2:14-24). *Perfect Harmony.*