Modern Orthodox, Dati Leumi, and Charedi: Are the Differences Halachic or Hashkafic?

Is “Dati Leumi” in Israel the same at “Modern Orthodox” elsewhere?
Is “Chareidi” in Israel the same as “Yeshivish” elsewhere?
What are their respective views of secular studies, engaging in the modern world, and serving in the IDF?
What are the most common misperceptions each has of the other, and what can each learn from the other?