Quite often certain people attempt to conflate trust and faith as if they are the same thing.
Trust is earned and subject to revision. Faith is not. Faith is expected without justification and is expected to endure regardless of what facts may come to challenge it.
I like your trust != faith comment. The two are similar and interrelated but not the same.
However, when you say "Faith is expected without justification and is expected to endure regardless of what facts may come to challenge it", I have to disagree. What you are describing there is blind faith.
Faith, as my comment tag line also says, is a willingness to accept something w/o total regular proof and act on it. From that perspective, every self-motivated action starts with faith. Getting out of bed to start the day, go to work, express love, turn on a car/computer, get on a plane, etc.), we make decisions and take action based in incomplete or uncertain information all of the time. However, science seeks to move away from faith and provides a systematic way to do so through the scientific method. Theories start from faith w/o proof--but then experimentation leads to the reformation or abandonment of that theory until repeatable experiments validate or falsify the theory.
Religion differs in that it never seeks to fully eliminate faith. Different religions (and to a higher degree, people) will rely on faith to different degrees than others, but ultimately each has at its core a non-falsifiable lemma. This kind of underpinning of faith is usually what some people find unattractive about religion. Some find comfort or wisdom in this kind of foundation based in faith. Note that science also has somewhat of a foundation of faith since it too uses lemmas, but it has a much higher restriction on what a reasonable lemma is.
IMHO, science and religion both have (or at least should have) the same end goal: the discovery of truth. However, both have different (and sometimes conflicting) methodologies to get there. But it's very important to separate the people claiming to be scientific or religious from science or religion in general since different people are better or worse at representing either than others.
To answer the original question: No, science isn't just a matter of faith. In fact, it is a systematic methodology to move away from faith.