There are people who, on Pesach, don’t eat anything that was produced outside of their home (with certain limited exceptions, like some people will buy wine or matzah from the store, while others will make their own; obviously, fruits and vegetables are not a processed food, but many people are makpid to peel them prior to eating). This minhag includes both processed foods and mishing, which are the same thing – as one is eating something that was not produced under his supervision.
If you eat processed foods, then you are by defintion mishing. It is the same thing.