Taiwan is an island off the coast of China, actually. I provided a link to a map below. China had a civil war back in the 1940s between communist and non-communist forces and eventually, the communist side won out. The non-communist government retreated off the coast to present ay Taiwan, and a state of war still exists between them. Mainland China claims today that Taiwan really belongs to them, and is just a renegade province.
No, Taiwan is not off the coast of Vietnam. It is off the coast of China. You can find this out for yourself by looking at the map that is in the link that I have provided below.
If you need to look up other places like this, you can just use Google maps. It will show you anywhere in the world, you can zoom in or out, stuff like that.
It makes sense that Taiwan should be off the coast of China because China believes that Taiwan is actually part of China. So the People's Republic of China does not recognize Taiwan as a country.