This seems very close to the stereotype content model, which asserts that every interpersonal impression is formed along two dimensions: warmth and competence.
Feeling someone cares fits the warmth dimension; commitment to excellence is a hallmark of competence. I would say the word trust can encompass both.
Trust is neither warmth nor competence - trust is the assumption that our mental model of the person we trust somewhat reliably predicts how they actually act, combined with somewhat aligned values.
Feeling someone cares fits the warmth dimension; commitment to excellence is a hallmark of competence. I would say the word trust can encompass both.
[0] - https://en.m.wikipedia.org/wiki/Stereotype_content_model