My interpretation of these findings is that the word "trust" is most often related to one's confidence in God's promises concerning what He will do in the future. He promised to send Israel a savior, and in Israel's way of thinking, that meant He would provide them with a mighty king, one who would conquer their enemies, and establish their nation as the seat of God's empire. Because their warrior king has yet to liberate them, they are still being asked to trust that God will send their Messiah to rule the world. He will (Rev. 20:1-7)!
As for the word "believe," it appears to me that it has more to do with what God has already done, or is doing, rather than what He will do in the future. The Gospels repeatedly call for Israel to put their faith in Jesus Christ; the writers present Jesus as the fulfillment of God's promise, using some form of the word "fulfill" 39 times in the Gospels alone, and 20 times in the rest of the New Testament. Of the 126 times the word "believe" appears in the New Testament, 46 of them are found in the Gospel of John! The only other New Testament books with the word "believe" in double figures are Matthew (11 times) and Acts (10 times).
In 1 Corinthians 15:1-4, the Apostle Paul summed up the revelation of Jesus, as He is presented in the Gospels: "Moreover, brethren, I declare unto you the Gospel which I preached unto you, which also ye have received, and wherein ye stand; by which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the Scriptures; and that He was buried, and that He rose again the third day according to the Scriptures."
As born again believers, that is, all who have believed in Jesus and His love for us, we also trust our Father will do what He promised He would do for those who accept His Son; we have:
Eternal life - Jn. 3:15; 5:39; 6:54; 6:68; 10:28; 12:25; 17:2-3; and
Everlasting life - Jn. 3:16; 3:36; 4:14; 5:24; 6:27; 6:40; 6:47)!