The difference is that the People's Republic of China (what 'China' usually refers to) has decided that the Republic of China has ceased to exist in 1949 (Taiwan is the last remaining territory controlled by the Republic of China) and that they are strong enough to largely 'enforce' this policy on the world stage.
So, of course for Chinese this is a domestic issue.
The West cares because the PRC is an adversary and Taiwan has a strategic location on maritime routes to East Asia.