No,
a Berliner is a donut, made from batter and normally deep fried. Muffins are cooke on a hot plate.
Not quite. Doughnuts are, given the name it's kind of obvious, made from dough not batter and are most definitely always deep fried (Although there's no doubt some Scots Calvinist vegan killjoy who's devised a way to make them from wholemeal chickpea flour without frying). Specifically it's an
enriched dough, enriched in this context meaning the addition of any one or all of fat, eggs, milk and sugar. Muffins are generally made from a
straight dough, containing just flour, water, salt and yeast. The best doughnuts generally have butter, milk and sugar in them, commercial ones tend to use cheaper, less tasty, vegetable fats.
Personally I can't tell the difference between a Berliner and a good doughnut. Knowing the Germans as I do, I expect Berliners are positively loaded with butter and all the other good things.