The US tax laws apply to any person who is considered a “US person for taxes.” That includes citizens (no matter where, in the world, they actually live) green card holders (no matter where, in the world, they actually live) and resident aliens (who pass the substantial presence test).
Of course, the $18,000 per person limit is only the limit to be required to file a form 709 gift tax return. Gift taxes never actually owed unless the giver’s lifetime gift total is more than $13 million.
