Faith in the sense of Salvation
Ephesians 2:8 & 9
Faith=pisteos
Thayer’s uses pistis conviction of the truth of anything, belief
Mounce states that this is firm belief
Henry=From Scripture it is clear, that whether men have been most prone to sensual or to spiritual wickedness, all men, being naturally children of disobedience, are also by nature children of wrath. What reason have sinners, then, to seek earnestly for that grace which will make them, of children of wrath, children of God and heirs of glory! God's eternal love or good-will toward his creatures, is the fountain whence all his mercies flow to us; and that love of God is great love, and that mercy is rich mercy. And every converted sinner is a saved sinner; delivered from sin and wrath. The grace that saves is the free, undeserved goodness and favour of God; and he saves, not by the works of the law, but through faith in Christ Jesus. Grace in the soul is a new life in the soul. A regenerated sinner becomes a living soul; he lives a life of holiness, being born of God: he lives, being delivered from the guilt of sin, by pardoning and justifying grace. Sinners roll themselves in the dust; sanctified souls sit in heavenly places, are raised above this world, by Christ's grace. The goodness of God in converting and saving sinners heretofore, encourages others in after-time, to hope in his grace and mercy. Our faith, our conversion, and our eternal salvation, are not of works, lest any man should boast.
Eadie=It is the uniform doctrine of the New Testament, that no man is saved against his will; and his desire to be saved is proved by his belief of the Divine testimony. Salvation by grace is not arbitrarily attached to faith by the mere sovereign dictate of the Most High, for man's willing acceptance of salvation is essential to his possession of it, and the operation of faith is just the sinner's appreciation of the Divine mercy, and his acquiescence in the goodness and wisdom of the plan of recovery, followed by a cordial appropriation of its needed and adapted blessings, or, as Augustine tersely and quaintly phrases it-Qui creavit te sine te, non salvabit te sine te. Justification by faith alone, is simply pardon enjoyed on the one condition of taking it.
Faith in the sense of Faithfulness
Galatians 5:22
Faith=pistis=faithfulness
Thayer=2. Fidelity, Fatihfulness
Mounce uses pistis as the word but uses the definition as faithfulness
Henry=faith, fidelity, justice, and honesty, in what we profess and promise to others
Eadie=πίστις—“faith” (“faythfulnes,” Tyndale, Cranmer)-not simply faith in God in the theological sense (Jerome, Theophylact),-that being implied, as the Spirit dwells only in those who have faith,-nor merely fidelity or good faith (Meyer), nor veracity (Winer); but trust generally, trustfulness toward God and towards man. Confidence in God, in all His promises, and under all His dispensations; and a spirit of unsuspicious and generous confidence towards men,-not moved by doubts and jealousies, nor conjuring
So we see in Ephesians 2:8 & 9 Faith comes for salvation, but Galatians says a part of the fruit of the Part is Faithfulness.
The Faith see in the fruit of the Spirit is not for Salvation but for our faithfulness in serving God and Trusting God in His promises. For instance Christ told the deciples that a little faith could move mountains. That is the type of Faith seen in Galatians 5:22 the Faith that God will work all things for good to them that Love Him. While saving Faith is a firm conviction in the efficacious work of Christ on the Cross. It comes when the Holy Spirit brings conviction, some respond and some reject. How do we know.
Genesis 4 and Cain, Cain believed God existed, he even offered a sacrifice. Abel not only believed God existed but Abel had placed his faith in a savior to come and gave an offering of blood to prove his Faith in the one coming. Cain was told to do good and thus follow God's command to believe and offer the proper sacrifice. We must believe that is have a firm belief in the Sacrifice of Christ and as Romans states call upon Him for that salvation and when we do we receive the fruit of the spirit which includes Faithfulness.