There’s an episode of one of the River Cottage series where Hugh and his forager friend go searching for puffballs… by taking binoculars to the top of a high hill. They find one that’s like, 30" across.
They aren’t the same sort, but there are mushrooms that pop up after some damp weather on the neighbors’ side of our driveway that go from being not there, then almost a sphere on a stalk, about the size of a baseball, and then they unfurl into dinner plates on stalks. It all happens very quickly when compared with starting vegetable plants from seeds. By the second day the tops are turning brownish and they wilt away into the grass.
Probably one and the same. The more mature they are, the more poofy. When they first come out of the ground they are uniformly firm and white throughout. Some species are decently edible - folks like to slice them into steaks, then bread and fry them. As they mature the interior breaks down into it is full of nothing but a bazillion spores - the poofy “smoke.”
By the time they get really large they are usually infested with tiny worms. But I once found a pristine one which I had to break in half to fit a piece of it into my day pack.
We get giant puffballs around here in my bit of Southern England - they’re quite highly prized by fungi gourmets - as long as the flesh is white throughout, they’re good it eat. Huge slices can be dipped in egg and breadcrumbs, then fried.
I’ve tried them and they’re pretty good - just big chunks of solid mushroomy stuff.