Throughout Ancient China's history, it often chose not to outright conquer and annex certain regions. The most well-known ones would be the kingdoms of the Korean peninsula as well as the ancient Southeast Asian kingdoms, which acknowledged Chinese superiority and would send tribute to the imperial court.

So the confusion tends to be around the term "ten thousand", or "wan" (万). The confusion appears to revolve around the fact that western observers assume it is literal, but the term "wan" is actually often used interchangeably in the Chinese language with "many".

For instance, the traditional greeting towards an Emperor, since the time of the first imperial dynasty, the Qin, was "huang di wan sui" (皇帝万岁), which literally translates into "ten thousand years to the Emperor", or "may the Emperor live ten thousand years". Now the Ancient Chinese didn't literally mean they wanted the Emperor to live ten thousand years, they were well aware this was impossible. Instead, it is simply a pompous way of saying "many", or "May the Emperor live many, many years!"

So, when the Qing Dynasty sent their message to the British, their meaning was simply that the Qing Dynasty lorded over many, many lesser nations, namely: Annam (present-day Vietnam), the Dzungars (parts of present-day Kazakhstan, Krygyzstan, and Siberia), Tibet, Kokand (parts of Kyrgyzstan, Uzbekistan, Tajikistan, and Kazakhstan), Joseon-era Korea, Lanfang (present-day Borneo), Lan Xang (present-day Laos), Nepal, the Ryukyu Kingdom (present-day Okinawa, which is part of Japan), Ayuthayya/Siam (present-day Thailand), Sikkim (part of present-day India), Sulu (part of present-day Philippines), Tuerfan (part of present-day Xinjiang Province, now a part of China proper), and Singapura (present-day Singapore).

Not quite ten thousand, but still an impressive amount of territory over which they claimed 'rulership'! Their hegemony was felt not just in China, but in Korea, part of Japan, Central Asia, Siberia, India, and Southeast Asia.

The Qing even received tribute from the Dutch and the Portuguese, and so actually regarded them as tributary states as well, to some extent.

Regarding the "China is the central kingdom but there are other kingdoms" part, one of China's ancient 'nicknames' you could say, was the Middle Kingdom. In fact, the modern-day Chinese name of China, Zhong Guo (中国), literally means "Middle Nation". This is because, much like Rome, China regarded itself as the centre of the civilised world. In the earlier dynasties, such as the Shang, Qin, and Han, China was indeed, the middlemost kingdom out of many other nations surrounding it, often considered 'less civilised'. By the time of the Qing Dynasty, however, most of those outlying 'Chinese' kingdoms, such as the Dali Kingdom, were conquered and annexed.

The term 'Chinese' is also a deceptively simple term. What does it mean to be Chinese? Is it to be under the authority of China? To be a Chinese citizen? To be specifically Han ethnicity? What about subdivisions within the Han ethnicity itself? It's a very complex topic that cannot be easily explained, and unfortunately with the use of terms like "Chinese kingdoms" without any proper definition of what makes them "Chinese", the waters get a bit muddied.

Hope that helps nonetheless.

References:

• A translation of Lin Tse-Hsu's letter to Queen Victoria, URL: http://acc6.its.brooklyn.cuny.edu/~phalsall/texts/com-lin.html

• Historical Records of the Five Dynasties (Columbia University Press), by Richard L. Davies and Ouyang Xiu

• A Recognition of the Status of Tributary System in Qing Dynasty, by Qi Meiqin