What is the difference between doughnut and krapfen?
There doesn't appear to be any difference. Wikipedia says "In English-speaking countries, Berliners are usually called doughnuts and are usually filled with jam, jelly, custard or whipped cream", and this page says "The English translation of krapfen is cruller or doughnut". There are so many variations of filling, topping, shape and so forth that it is hard to establish a single identity anyhow.