To be sure, the two words are related. They are essentially synonyms. In the Bible, faith means to trust in God; to believe that God is who He says He is and will do what He has promised to do. The Bible says, "Now faith is the assurance of things hoped for, the conviction of things not seen"(Hebrews 11:1).
I think the folks at the CARM summarize the relationship between faith and trust well when it comes to our Christian life. They write:
"Faith does not save you. Got that? FAITH DOES NOT SAVE YOU! Faith is not a substance that you put in a jar or detect with a meter. Faith isn't a cream you apply to protect you from something. Faith is belief, trust, etc. The key to understanding faith lies not in faith itself but in the OBJECT of faith: God! Faith is only as good as who you put it in. Faith in a false god (i.e., Mormon, Jehovah's Witness, etc.) is useless and it doesn't save you. But faith in the TRUE God DOES save you. You see? Faith is only as good as who you put it in. Faith in the true God results in salvation (Rom. 5:1; Eph. 2:8). Faith in a false god results in damnation."
[Answered by Pastor HM, who has faith and trust in Christ]