You ask: "Then why is faith, trust, and believe usually the same greek word in the bible?"
I will let you study that and figure it out. Why would that bible verse use two different sounding words that mean the same thing when they could have just used the same word twice? I don't know.
Probably because it's all part of salvation. You can't have faith without belief and you can't have trust unless God gives you faith. Besides I'm not taking the word of a book writer/president of a ministry to give the final word on that without some more study.
The scripture seems to say that whoever would draw near to God is someone who must be seeking....and scripture says that God rewards those that seek. I would say that Holy Spirit is drawing him...wouldn't you? However, drawing him and gifting him would be two different things.