What is the difference between how nut flours and nut butters are made?

It is both, depending on what you understand under "nut flour".

The first kind of "nut flour" is something that may more precisely be called "nut meal" or "ground X" (where X stands for the nut, as in "ground almonds"). Nut meal is simply nuts reduced to small particles (larger than flour particles though) and is created by cutting up the nuts with bladed machines. You can make it at home in a food processor.

The second kind is true nut flour. It has finer particles, good water absorption, and behaves more like an actual flour in baking. For that product, they de-fat the nuts, and then I assume they actually grind them up instead of using a bladed machine. I am not entirely sure how these flours are produced, AFAIK there is no way to make them at home.

Nut butters are created by grinding in a mill, using actual shear force and not cutting, and may need adjusting the ingredients by adding more oil, but that depends on the nut, with e.g. peanuts grinding up nicely without needing extra fat.

I also suspect there may be a difference in water levels, with nut butters working better with fresh nuts, nut meals getting no special processing (but they do dry out quickly after grinding) and true nut flours probably needing a dehydration before they can work well. This is more of an intuition of mine, I don't know if producers actually have to do it that way.