Can anyone tell me if there is a difference between mistrust and distrust and if there is what is it? If there is not why are there two words with the same meaning and the same obvious root?
'Mis' and 'dis' have roughly the same meanings but the former is derived from early English whereas the latter is derived from early French. The English nobility would have spoken French in mediaeval times. (It was the official language of English courts until 1731). Peasants would have spoken English. So 'distrust' might be thought of as the 'posh' word, whereas 'mistrust' is the 'common' version.
mmmm.... Chris's explanation is historically sound, but I don't think there's any such difference today.
You often get words with the same meanng that have come from different sources - eg royal and regal, one from Latin via French and one more directly from Latin. Linguists call them doublets, I think.