Works pretty much the same in the US, too.

When we pay US contract labor, we generally send the "gross cash amount". The US contractor actually has to fill out a form upon commencement that says how their taxes & social insurance will be paid; at the end of the year they get a form from the businesses they did work for which shows total paid, and they use that to do their taxes.

Same thing for international contractors -- they just have to deal with their local jurisdiction's taxes, instead of the US IRS.