Trust and faith are different, I believe. I think faith comes before trust, before proof of trustworthiness. Once your faith has been "proven" through actions, you can trust. But trust is based on actions.
To name an explicit example, imagine, for a moment, that you are stranded on the highway in a snowstorm and you call AAA. It's your first time calling AAA and you have no background to predict when or if they will come, but you have faith they will. If they do end up coming, trust begins to grow. If something like this happens again, you trust that AAA will come through, because you now have evidence for your faith.
To simplify, then, faith is trust before evidence and trust is faith after evidence.
Faith, though, is not irrational. Keeping with the AAA example, you can go online and read reviews and have some reasons for your faith, which are not evidence (because they did not happen directly to you), but are still trustworthy and logical.
Trust then, seems a very personal thing. I feel we can only trust through personal experience and therefore any trust is an intimate thing we must be careful with and mindful of.