Are 中国 and 中华 synonyms? For example, Chinese Taipei can be translated either as 中国台北 or 中华台北。Are 中国 and 中华 synonyms?

If there is any differnce between 中国 and 中华，how to reflect the difference in English translation?
In Modern Chinese, 国 means a sovereign state, e.g. 中国, 英国, 美国, 德国, etc. In ancient times, 国 could also mean a non-sovereign state, e.g. 楚国, 齐国, 赵国, etc. Anyway, 国 emphasizes the government's control of a specific land.

As a result, 中国 can only refer to the sovereign state that is named China, while 中华 is more likely to refer to the ethnicity or nation that is named China.