Does relate to the point that English still doesn't have a central linguistics authority (and likely won't ever). Just various reformers that have been more or less successful and in how distributed their reforms have been. Draught versus draft was indeed one of Noah Webster's proposed reforms that influenced a lot of American spellings and in turn is still influencing UK spellings. It's not as obvious as color versus colour, but there is a bit of US versus UK in draft versus draught.

(Webster also went on to suggest dawter over daughter, to remove more of these vestigial augh spellings, but that one still hasn't caught on even in the US. Just as the cot/caught split is its own weird remaining reform discussion.)