resistivity is a constant for a substance that depends on what the material is made up of. It's an index number so we can compare two substances. What are we comparing? How much energy is lost when electrons are moved from one area to another or how much that substance opposes the flow of electrons. The higher the resistivity, the more "energy" is lost.
Resistance is a measure of how much "energy" is lost for a resistor. But for the MCAT, you can think of resistance as a proportionality constant. For a given resistor, if there is a potential difference of X, you can calculate how much current flows through it.
Resistors are made up of different substances and have different lengths/cross sectional areas. All three factors play a role in a resistance according to your first equation.
Another way of looking at it: If we're building a resistor, we would use R=pL/A because resistance depends on the resistivity constant of the substance, its length, and its area. If we had information about a resistor in a circuit, we would use Ohms law.
