Trust is relational and involves reliance of one on the other, individually or in groups. The reliance is based upon the non breaching of trustworthiness of the one trusted. Trust is past base but mostly future oriented. Trusting someone called trustee to take care of asset disposal after death requires lots of assumption after the truster's death is future oriented.
Belief is a mental state of a person holding a premise to be true. It is knowledge based but it is not the same as knowledge, which is justified true belief. Belief is tentative in holding something to be true, but the believer may trigger this tentative thing into thoughts and thoughts into action, and the resulting action is neither based on facts nor on justifiable truthfulness of that belief that triggered action. Going to war based on unjustifiable belief is risky stuff. Firing someone based on fear, that a common cold may deteriorate into something horrifying is unethical and illegal.
Faith is based on unproven belief. Faith is formed by a leap of faith. It is not recognized by the holder as tentative but as if the reliance on a person, a thing, a notion, a deity, is truth or even absolute truth.
Faith requires also the complete trusting of the item to be trusted and the complete abandonment of the person's own freedom of choice, and if there exists doubt, the holder of faith is called agnostic. This is the most risky type of belief, like going to war based on belief is risky, but going to war based on faith is even more so. If trust may be built between potential warring parties, trust must be the choice, at the expense of belief and faith. Hence belief and faith are closer to each other and both are further away from trust. If an expert dismissed this kind of dichotomous polarity, the expert is lacking in clarity and if he or she were to continue holding this polarization to be a false duality is probably himself or herself confused by mistrusting reasons proposed and is overly relying on own belief which is not yet justified but by the heat of his or her pant in sighting something such as a mono name.