In a language where some words are also their own opposites, it can be hard to remember the subtle differences between all the nearly identical pairs of terms, from historic and historical to disinformation and misinformation.
In the case of mistrust vs. distrust, you can technically use them interchangeably without fear of being corrected. As verbs, they both basically mean “to be suspicious of” or “to lack trust in;” and their noun forms similarly mean “suspicion” or “a lack of trust.” Even the most well-respected dictionaries use the terms to define each other. The Oxford English Dictionary describes mistrust as “to be distrustful,” and Merriam-Webster lists distrust as one definition of mistrust. If you’d prefer to favor the older option, mistrust wins by several decades: According to the OED, it appeared in print as early as the 1380s. The earliest known reference to distrust didn’t come until 1430.
Although mistrust and distrust are essentially lexical twins, they’ve evolved with their own separate connotations. These days, as Grammarist explains, distrust often implies a lack of trust predicated on previous experience or knowledge. Mistrust, meanwhile, implies a broader absence of confidence that doesn’t necessarily stem from something specific. If your fourth grade teacher had a tendency to misspell words and mix up facts, you might start to distrust whatever they taught you. But if you, as a kid, had a general sense of suspicion toward all teachers, coaches, and other adults in your life, you could say that you mistrusted authority figures.
You could even make the argument that distrust better applies to situations where something caused you to lose trust; while mistrust refers to a lack of trust where there never really was any to begin with. It’s more a product of the atmosphere than of the past. But, again, these distinctions are based on general trends in modern usage, rather than any hard-and-fast rules.