It's a fact that American English and British English has some differences in meaning and spelling. For example, Americans write 'center' while the British insist it's 'centre.' Moreover, rubber in British in eraser while in American English, it has some references to reproduction. What about donut and doughnut?
This has been a subject of debate not only among people, but dictionaries and style guides. Even stores that sell the stuff seem like they're out to prove which one has the correct spelling as well as the better tasting donut or doughnut. For example, Dunkin' sells donuts everywhere but Krispy Kreme sells doughnuts.
Even dictionaries can't agree but Merriam-Webster says that donuts is a variation of doughnut. They mentioned in their blog that the word 'donut' has been in edited, written text since the 20th century. Even Benjamin Franklin and Noah Webster has used this spelling which was based on phonetics.
Aside from this, the growth of Dunkin' Donuts and Mister Donut has made the spelling even more popular. It makes sense because when Dunkin' Donuts opened in 1950, it started franchising in 1955 until its shops grew to 100 across the nation in 1963. After more than a decade later, it had 1,000 stores. Mister Donut, on the other hand, is in 10,000 locations all over the world.
Although the use of 'donut' has become more popular over the years, the word doughnut is still used by a lot. Thanks to the spelling constraints imposed by style guides. In fact, the Associated Press has directly addressed the issue in 2013 according to Business Insider. The AP style made it clear when it mentioned that 'donut' is a brand name but the food item should be spelled as 'doughnut.'
Despite this, a lot of stores worldwide are willing to follow Dunkin when naming and calling it donut. It doesn't really matter unless you really have a problem with it and that you have to write for a publication which uses the AP Style guide.