There’s no actual difference in meaning/etymology between ‘Diets’ and ‘Deutsch’. They’re both derived from Proto-Germanic *þiudiskaz, meaning ‘of the people’. Well into at least the seventeenth century, probably the eighteenth (I’m basing this off what I’ve read myself in primary sources) ‘Duits’ was still commonly used in the Netherlands as well. It was essentially part of a distiction between ‘Duits’ and ‘Waals’, where those who were ‘Waals’ were the ‘others’.