Many definitions exist and the borderline is extremely fuzzy. For instance the 80C86 is considered a uP and the 80c186 is considered a uC.

Here are some definitions I have heard, none are absolutely correct.
1) A microprocessor (such as x86) is supposed to be used in places (such as a PC) where it does various things, a microcontroller is supposed to be used for one thing (such as a scale, a power controller, an analytical instrument etc)
2) a uP has code in RAM, a uC has code in (E(E)P)ROM
3) a uP has no I/O on the chip save the bus, a uC does.
4) a uP has an instruction set optimized for arithmetic, a uC has an instruction set optimized for logic.

The real question is not uC vs uP but the right device for the job. E.g. the
'51 has a powerful bit handling instruction set, the x86 doee not but has a better multiply/divide.

There is no solid answer to your question, this is probably as good an answer as you will get.

Have fun, do not worry whether uP or uC.

Erik