Actually not we have the IS300 too its one of the cheapest ways to get a 2jz over here the is200 is a 2.0 liter version more like a base model and the is300 is the sporty high end model
Not just a nickname, "Altezza" is the actual name of the Toyota-badged version of the Lexus IS sold in Japan and select asian markets, much like the Lexus GS was known as the Toyota Aristo were the Lexus brand wasn't available.
200 and 300 after IS (the model name) are trim indexes that specify the engine size. Both are international models.