Because the actions are different. For example, I work with a lot of people who are overpaid dopes. I'm shocked that some people have made it as far up in the organization as they have. I don't "respect" them because I think they're not very good at what they do - don't know how to access resources, don't follow through on details, miss opportunities, can't do things for themselves, etc.. But I trust them - I know that they are good people, are honest, fair in their dealings with clients, will admit to and correct mistakes, adhere to our code of conduct, and are overall, trustworthy and ethical people. They should just find different careers.
My husband and I have issues of both trust and respect regarding each other. And even with our kids, there are things about his parenting style and choices that I don't respect and am pretty openly critical of. But I trust that they are safe with him and that he has their best interests at heart when it's important.
I think a lot of couples who split up have to get to this point - they have to trust their ex with their children, but might not respect him or her in any way, shape or form.
On the other hand, someone can show you respect and still not be trustworthy because of their own failings. My oldest son's birth father put me up in a pedestal, worshiped the ground that I walked on and in his own weird way was super respectful but that didn't change the fact that he was a con, a fraud and a liar through and through. It was like "as great as I think you are and as much as I love you, I am incapable of being honest."
So I think it's a bit foolish to trust someone merely because they respect you, or not trust someone because they disrespect you. The other person may have a perfectly valid reason for disrespecting you, it doesn't make him or her not trustworthy, kwim?