Looks like Saiix integra 'Hakuro Nishiki' in its late summer coloring (loses all the pink tones, generally, and is mostly just green with some white splotching).

Ok this willow is clearly over its mature size. It’s at least 12 ft tall by 25 ft wide and Missouribotanicgarden has it 7 ft wide.. not sure why all these websites get plant sizes totally wrong. I was going to take cuttings from these and grow it in my boggy area but looks like I would need a lot more space than any website tells you too

Most folks hard prune shrub willows pretty regularly (much like they do shrub dogwoods), so easy to keep the size within bounds. Supposedly intensifies the early spring variegation as well. The species itself can grow to 6 meters or slightly more with an equal spread and according to Whitman Farms, "This Japanese willow will have an equal spread and height and can reach 20' by 25' at maturity."

"not sure why all these websites get plant sizes totally wrong."

They don't.

The sizes you are seeing are ten year estimates to give you an idea about what to expect as far as growth. The plants in no way stop growing at that point.

I will have about 25 ft of space to spare where I want this willow but anymore than that will be an issue! Guess I will regularly prune them once they reach a good size to do so.

I wish websites can give you at least 40-50 year estimates of plant sizes, otherwise it can come off as misleading and after that many years you find yourself out of space and either remove the plant which is a painful process or severely hacking them which can't be healthy. I know you can do the math by growth rate but certain plants start slowing down after a certain amount of years and one cannot tell when unless they lived that long along with it.

Few people stay in the same home for forty or fifty years so they're probably not interested in those figures. And, as gardengal said, most people coppice or pollard these willows to improve colour. The one in the photo has been pruned.