They are all words made up from parts of words, word beginnings with exact meanings. Differ means not the same, to vary means going to others and diverse expresses the notion that you're going down some other highway; they are close in meaning but not synonymous, the beauty of English is that the vocabulary is a big mix of several older languages including a lot of words from French and German. This vastness gives the language a richness and allows us to choose the precise word to deliver exactly what we want to say. Good Q!