"Trust" in the Hebrew בָּטַח (batach), means "to trust," and it occurs 120 times in 117 verses in the Hebrew concordance of the KJV.
"Trust" in the Greek πείθω (peithō), means "to have been persuaded," and it occurs 63 times in 55 verses in the Greek concordance of the KJV.
"Believe" in the Hebrew אָמַן ('aman), means "to trust," and it occurs 108 times in 102 verses in the Hebrew concordance of the KJV.
"Believe" in the Greek πιστεύω (pisteuō) [from the root πίστις (pistis) which is translated "faith" 239 times in the New Testament], means "to have faith in," and it occurs 264 times in 220 verses in the Greek concordance of the KJV.
An illustration of how the words "trust" and "believe" differ only in timing, can be seen in a born again Christian's prayer life. When we approach the throne of God with a need, we trust that He is able to fulfill our request. We trust that He loves us, and that He only wants what is the absolute best for us, His children. We know in our heart that He will only "say yes" to our request if it is what is best for us (Rom. 8:28-29). And, we also trust that He will "say no" if our request is not what is best for us (Rom. 8:26-27). After we have prayed, we believe that He has heard our prayers, and we believe that whatever God chooses to do, it will work to make us more like Jesus (Rom. 8:29; Eph. 2:10; 4:11-16; Phil. 1:6; etc.).
When we truly trust and believe in Jesus, repentance happens!