" I can't seem to get my head around something that is '13mm' in size will accept someting that is '10mm' in size."
A nut can be measured by two dimensions, the size of the hole in the middle and the distance apart of the opposite flats on the hexagon that surrounds the hole.
The standard wheel stud is an 8 mm rod, with a thread cut into the surface.
The standard nut for an 8mm bolt is 13 mm from the flat on one side to the flat on the other side. It has 2.5 mm of metal around the stud.
One can use a nut with only 1 mm of metal around the stud, so it is only 10mm from one side to the other.
So one isn't fitting " a 13mm that will take a 10" but a nut with an 6.75mm hole and a thread cut out to 8mm which fits on stud of 8mm with a thread cut in to 6.75mm and differing thicknesses of metal wrapped around the hole!
However a nut of only 10 mm diameter is likely to wear holes through the alloy of the wheel centre quite quickly, so we use Flanged nuts, that expand to a wider diameter below the hexagonal bit. This doesn't stop the centre from wearing but it does make it much slower.
We use K nuts because they have the thread distorted so that they are 'tight' when they are done up, and when they get loose with use, hitting them with a hammer squeezes the thread back into a distorted shape.
Good engineers only use a K nut once, just as one should only use a nyloc once. In practice they are often used more than once.
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