Depends on several things:
1. Physical lay-out of your room. With me, at home, the TV is on one side and the PC on the other. That would make it very unpractical to use the TV for PC work. So I've got a TV and a monitor (with the added advantage that my wife can look TV while I'm sitting behind the PC).
2. Viewing distance. A PC monitor usually is viewed from 20" or so. A TV from, say, 2 to 3 yards. That's why a HDTV usually is 32" or bigger and a computer monitor 20" or smaller.
3. Reception of signal. A TV comes with a tuner built in. To view TV on your PC you'll need a tuner card in the PC (or only view via Internet) and use a monitor.

In fact, there's not much difference between a 20" TV and a 20" monitor, apart from the fact that the TV has the tuner built in and can be used as a monitor also. And, of course, the TV comes with a remote. While on the other side you can use your PC as a hard disk recorder.

If you feel happy to look television sitting at your desk without using a remote it doesn't really matter how it's called.

Kees