As the name suggests, a national highway is one that caters to only regions within a nation. In comparison, an international highway will cater to regions in multiple countries. An example of a national highway is the I-5 in the U.S. that runs from Washington to California. An example of an international highway is the newly proposed highway connecting India and Thailand, via Myanmar. A national highway will never cross the international border of any country, while an international highway will. A national highway only has to confirm to one nation's rules and regulations, regarding the construction, dimensions, driving rules, speed limits, etc. In comparison, an international highway will have to confirm to a common set of rules & regulations, or those of all the countries through which it passes.
Hope this helps.