Seems to me that the difference between distrust and caution is one of identification, and/or boundaries.
If I am talking about my responsibility to protect my own interests, I am talking about caution.
If I am talking about the possibility of someone else doing something against my interests, I am talking about (dis)trust.
I hypothesize that in any situation, whether the people involved talk about trust or caution is really about whether they are placing responsibility on themselves or on someone else.
And so for people who have unclear boundaries and/or unclear language around such situations, those words can become loaded with unpleasant or unfair connotations, at the same time that they may likely be being used to move responsibility and control back and forth, and probably unconsciously framing it in terms of these labels. But it’s really about assigning responsibilities and contracts, and agreeing to them. Misuse of the words by turning it instead into something like “no it’s an issue of trust!” is an (often mistaken) attempt to assert that one perspective is just right, usually because sloppy thinking is resulting in looking like a justification for a position that puts responsibility on the other person, and/or puts one person in control, or shames the other person while avoid shaming the speaker, or whatever.