Most of the time, when a western based news media show a map of China, they will show a picture similar to this.
And when mainland Chinese news media show a map of China, they will show something like this.
The biggest difference between the two (besides the colour) is that the first map does not include Taiwan as part of China, where as the second one does. If you were to ask a western which is correct, they would say it is the first one, but if you were to ask the same question to a citizen of the People's Republic, they would choose the second to be correct, and both would accuse each other of being the victims of propaganda by their respective governments and media.
Now if you were to ask me which map would I choose to be the most accurate, I would choose the latter. Now before you accuse me of being the victim of communist brainwashing, I would like to clarify that even though I do agree with the second picture, but I also believe it be too simplified. The most accurate picture of China, I believe, would be this one.
The fact of the matter is that, despite the peace and interaction between the two sides in this day and age, the Chinese civil war has never really ended, with the People's Republic of China (PRC) controlling the whole of the mainland, and the Republic of China (ROC) controlling Taiwan and a few small islands off the coast of Fujian province. In a sense, Taiwan is independent from the People's Republic of China, as it has sovereignty over it's own lands and it runs its own affairs without interference from Beijing. But being independent from the PRC does not mean that Taiwan is not part of the same China as the Peoeple's Republic. Both the Republic of China and the People's Republic of China are part of the same China, in the same way that the Qin, Han, Tang, Ming, and Qing are all part of the same China.
The conflict between the Chinese perspective and the western perspective is that westerns view nations though the lens of the nation state, they will see all of the different dynasties as being different nation states, whereas the Chinese will view all of them as being part of the same nation, just with different rulers. Thus, for westerns to simply accuse citizens of the PRC of being brainwashed is not only extremely arrogant, but it is also ignorant as well.
You would be hard pressed to find a PRC citizen who thinks that Taiwan is under the rule of the Beijing government, they are not ignorant to the situation between Beijing and Taipei. When they say that Taiwan is part of China, they are not claiming that Beijing has sovereignty over Taiwan, they are simply saying that the Republic of China, and the People's Republic of China are part of the same China and the difference is simply a difference in ideology.