Why was the Rebbe so enthusiastic about the term trust? Indeed, what is the distinction between trust and belief?
Imagine a tightrope walker who has carried members of the audience on his back across the tightrope. He turns to the audience and asks, 'Who here believes that I can carry them across the rope on my back?" Considering that the audience has already witnessed him performing this feat, the majority of them, including you, raise their hands in the affirmative. He then points at you and says, "OK then, I'd like you to get on my shoulders and be the next to be carried across." Your heart suddenly erupts with fear and you diplomatically smile while declining with an emphatic, "No Way!"
If you believe that he's able to carry you across safely, why don't you allow him to? Herein lies the often enormous chasm between belief and trust. You believe him but cannot put your trust in him. Trust is the quality that enables one to overcome fear in practice, and in its complete form extinguishes fear altogether.
This explains the Rebbe's excitement about the statement, "In G-d we trust." Many people believe in G-d and even in His all pervading providence. Yet, when times are tough they are overcome with anxiety and depression. One who trusts in G-d, however, walks securely and confidently.
This difference between belief and trust is highlighted in skateboarding. When I arrive at a skate spot, I typically look around at the obstacles available and assess what I believe I can use and what is yet beyond me. Frequently, I believe I can easily perform a semi-dangerous trick such as jumping off a set of 5 or 6 stairs but as I ride up to the stairwell edge I'm prevented by fear. Based on my past skating experiences I authentically believe myself capable of easily landing this particular stunt; my lack of trust in my abilities, however, opens the doors wide for fear to engulf me in practice.
Belief relates to mind; trust relates to action.