mistrusting distrust

A law school friend messaged me today to ask the difference between "mistrust" and "distrust". We'll ignore the irony of a lawyer asking an engineer for vocabulary advice, for today.

My first answer was that they were much the same, except for a slight difference in connotation (which I couldn't describe), but that "distrust" was worse. We both agreed that we used "distrust" more often.

My second answer, obtained using Google, was much more informative. Here it is, courtesy of the Columbia Guide to Standard American English:

Mistrust means “to doubt, to lack confidence in,” as in I mistrust his ability to persuade her. Distrust means much the same but adds suspicion to the mix: He distrusts her because he thinks she’ll cheat him.

It appears that both of us are thoroughly cynical modern women.