Taiwan, (Technically called the Republic of China) is an island about the size of Northern California. Population is around 20 million and still one of the strongest economies -- 22nd in the world! Note on the second map that it also includes a number of small islands including some in sight of mainland China.
Taipei is the main city or the "New York" of Taiwan. The Southern City of Kaohsiung would be the Chicago with 2.8 million population -- the major port of Taiwan and a booming economy and business spirit!