The international contractor recieves a 1042-S and at the end of the year the US company would file the annual report 1042 to summarize all of the 1042-S they filed.
The american company would report of these payments under its quarter 941s and its annual 945 returns.
The foreign contractor gets a 1042S at the end of the year and would have to file a 1040NR to get a refund of their taxes withheld.
its an insane and complicated process but its all so that the IRS gets their fair shake. Most companies should be wary of hiring offshore because its actually a butt-ton of work but they never know these things until its too late.
The real horror story is that this is considered payroll tax and you're ALWAYS personally liable for these taxes. Thus, any company shareholder, director or executive is personally liable for these taxes. They can levy your bank accounts anytime for restitution.