A Resistor does the same thing as a potentiometer, only it has a fixed value, right?
Wrong. Your statement would be correct if you replaced 'potentiometer' with 'rheostat'.
A potentiometer is a variable resistor.
That's not exactly right either. Your statement would also be correct if you replaced 'potentiometer' with 'rheostat'.
At the risk of over simplification:
A resistor has two terminals and has a fixed resistance between those two terminals.
A rheostat has two terminals and you can adjust the resistance between those two terminals. So, a rheostat is a variable resistor.
A potentiometer has three terminals. It has a fixed resistance between the end terminals and a variable resistance between the center terminal and either end terminal. A potentiometer is essentially a variable voltage divider.
So, for LCD contrast control, there really is no way to replace the recommended three terminal potentiometer with a single two terminal resistor. There are those who claim to have conjured up 'solutions' using a single resistor or a single diode that have supposedly worked in certain cases, but I suspect a wad of bubble gum would have also worked in those cases.
You could try connecting pin 3 to GND. That gives a usable, but not optimum, display in some cases.
If that doesn't work you might be successful using two resistors. Try something around 10K between +5 and pin 3 and around 1K between pin 3 and GND.
Don