OK, I was asking about trust, I guess you can throw belief into the mix.
That's what believing is......trusting God. Believing is not just knowing something is true. That's faith. Faith comes from God as a gift. Believing is when you take what you know is true and place your trust in it. You do that.
But it sounds like you are making the distinction between verb and noun forms....
Not necessarily, but that's a good place to start. Faith is a thing. Believing is a verb. Though that's not a hard and fast rule.
....not in meaning. And looking at the Greek, are you finding different words used?
No, you won't learn much through a pure word study. Just look at how the secular world throws the terms 'faith' and 'believe' around. The Bible does the same thing. Context and intent are the rule of interpretation here. Faith is the supernatural ability to know something is true. That comes from God, entirely at his discretion, according to his mercy. Believing is you then trusting in the thing you know to be true. You do that. God gives us the faith....to believe.
Justification occurs when you believe in what faith has shown you to be true. I think many people take false comfort in thinking that just knowing the gospel is true saves them. No, it's when you trust in the gospel you know to be true, that's when salvation occurs. Took me about 4 years to finally give in and trust in the gospel that God was showing me is true through the testimony of the Holy Spirit.