1861 Donutty

I wonder sometimes how we end up using some of the words we do. And sometimes the etymology dictionary is no help.
Like the other day I was driving by a donut place. The interesting thing was, they couldn't decide on how to spell the word. One sign on the building said d-o-u-g-h- nuts and the other said d-o- nuts.
So which is it? Is the d-o- donuts like the thru in drive thru? T-h-r-u- instead of the full t-h-r-o-u-g-h-. The d-o- just a contraction for d-o-u-g-h-? If so, where is the apostrophe?
Even more confusing if you ask me, is in just about every other word in the English language where d-o- appears it's pronounced "dew," as in Dudley Do-right. So why aren't they dew-nuts?
They are often sweet as the morning dew.
I understand the dough part and the spelling of d-o-u-g-h-. Both because they are made of some sort of dough before they're fried and because you have to shell out some dough to buy them.
But what is the nut thing all about? I know some doughnuts are covered with actual nuts, but usually they are described as nut covered doughnuts. What is it about frying dough that causes it to be some sort of sub-category of the nut genre?
They don't taste nutty. They don't crunch nutty. We don't treat doughnuts like real nuts. We don't salt them and roast them. Or shell them for that matter. We don't chop them or sliver them or crust the top of entrees with them. "Ah, delightful, a doughnut-crusted pork loin..."
And we certainly don't render them into a paste. I don't believe I've ever heard of doughnut butter. Yes, there are jelly donuts.
But I've never seen a doughnut butter and jelly sandwich.
America, ya gotta love it.