If you want a bolt with the same threads as the lug nut, it will be either a SAE standard bolt or a metric standard, and will most likely be a medium to fine pitch. e.g. 7/16-20 (UNF), 1.25 mm pitch for metric 10mm or smaller, 1.5 mm pitch for larger 12mm or 14mm stud sizes.
Automobile studs and lug nuts have been metric for a long time, what is on a trailer will depend on where the manufacturer sources the parts.
Carriage bolts are a different kind of fastener, made for a different purpose, with sizes and thread pitch from a different era. For each of the ten sizes of carriage bolt, there is usually only one pitch, UNC standards.
I usually find the nuts and bolts I need at a farm supply store, as they tend to have lower prices than the auto parts places or the big box lumber and hardware chain stores, which might require me to buy a half dozen pieces when I need just one.
