Various textbooks and other sources have conflicting information. One book I read said that China "handed over Korea and Taiwan to Japan" in 1895, which brings up 2 points of confusion: If this is correct, why was Korea not officially annexed for another 15 years, and how was China able to do this if Korea was a sovereign state as is suggested by other sources?
Joseon Korea was under a nominal tributary relationship with Ming and Qing China. For example, the Korean Kingdom would send envoys to China 3 or 4 times a year and notify the emperor if there were any changes in government like when a new king was crowned. The book you're reading likely has done a very bad job of explaining the East Asian political system that was arguably at its height during the Ming and Qing.
Simply put, tributary relationships and nominal recognition of Chinese primacy in East Asia was necessary to have relationships with the Chinese Empire. Korea, Vietnam, Ryukyu Kingdom, South East Asian polities were all nominal vassals of China, as were the British, Dutch, and Portugese Empires. China at the time basically saw anyone who presented them with envoys as their "tributes" regardless of the realities of power relations at the time.
This makes it seem like I'm downplaying Chinese influence on their neighbors especially in regards to Korea. There is no doubt that China was culturally influential in Korea and Korea accepted Chinese primacy (though this did degrade quite a bit with the rise of the Manchu led Qing). This is the reason why Korean monarchs were kings and not emperors themselves. Emperor in the East Asian context implied equality, which China would not allow any challenges to (with the notable exception of Japan). However, historically China has chosen to not exert its political influence over Korea in what scholars have termed "benign neglect" which has allowed Korea to develop as a sovereign nation throughout history.
The result of the First Sino Japanese War was a change in "tributary" relations. Taiwan in this case was handed over to direct control to Japan, but Korea was instead removed from Chinese sphere of influence and installed with a reformist pro-Japan government. It sounds like your book didn't make the distinction between direct and indirect control.
Removal from the Chinese world order allowed Korea to declare itself as the Korean Empire (Daehanjeguk), not Joseon which was a name approved by the Ming Emperor which shows the word "Empire" is misleadng in a sense because it's not what we think of empires in Western historiography. This declaration of Empire meant the equality in Korean-Chnese relations and allowed the last king of Joseon and the first emperor to wear yellow robes which outwardly signified sovereignty to China as seen in this portrait here: Emperor Gojong
Korea was historically a functionally sovereign nation with nominal tributary relations with China, so I can see why it's difficult to dissect the Korean-Chinese relations in just a single sentence. This relationship has been muddled by nationalist historiography in East Asia, which range from total sovereignty to total vassalage to China. China could hand over Korea in the sense that it left its sphere of influence but could not hand over direct control of its territories to Japan as was the case in Taiwan.
Japan's indirect control over Korea through the installation of a pro-Japan government (under the guise of being pro-reform) was the reality from 1895. Annexation was merely throwing away those pretensions.
Sorry, this was a lot longer than I intended it to be. Thought I could answer in a few short sentences, but I guess not. If there were any unclear bits, I can elaborate further.
