A King size bed is larger than a California King. California King's are longer and narrower than traditional kings and the total surface area is a little smaller.
Less common, but Wyoming Kings and Alaska Kings are bigger than either.
I searched for "Complete Sheet Sets, 600 or higher threadcount, Egyptian cotton" and then looked at the sizes available, they all only went up to King/Cali King.
Oh, yeah, they're uncommon enough that you prob gotta start from "Wyoming King Sheets" and then narrow down from there on type rather than vice versa, and possibly compromise on the material you get if it's gotta be from Amazon.
Honest question. I have a full size bed, but if I buy a queen size fitted sheet, doesn't that defeat the purpose of a "fitted" sheet? Not even asking for a friend, asking for me. ;-)