What is the difference between a resistor and a heating element?
A resistor and a heating element are indeed the same thing, just designed for different jobs. In a resistor, heat is generated as an undesired (but unavoidable) side effect, whereas in a heating element, the heat is exactly what it's supposed to do.

In fact, resistors can be used as heating elements! I've seen at least one ovenized oscillator (where a tiny oven is used to keep one component at a very specific temperature) that simply used a resistor as the heating element.

One difference that does exist, though, is that heating elements are generally made of materials that will work at higher temperatures. They're supposed to get hot, after all! Resistors usually aren't as heatproof.