Let's get into it:
The difference between Resistance and impedance is
Resistance is dissipation of energy in the form of heat
Impedance is NOT dissipation of energy, it DOES NOT reduce power, it is a phase variance in the TIMING of power, basically. You may see less power from the DMM measurements but the energy is stored in the softparts while they are moving.
Impedance is the general term we all go by. The voice-coil's Raw resistance of it's wire is NOT impedance. People also get that wrong. The nominal Impedance is a value that is CLOSE to the coils raw DCR value.
Rise is with both resistance and impedance.
As I said before, impedance is a phase varying thing. When you push someone on a swing it takes alot of energy from you to push their heavy but into the air. If this was resistance that dissipated energy or "wasted" it then as soon as you pushed them they would stop in the air and wouldn't swing back. Physics dosn't allow them to just stop in mid air because of their weight. Subwoofers have weight so obviously they are energy storage devices. This is the difference between resistance and impedance. Subwoofers want to keep moving when you send them power/signal. The box/design you use will vary how much they want to keep moving at a given frequency or harmonic played through it after the signal is gone.
So, the resistance comes from the voice-coil heating up, and to a lesser extent some real world losses in the parts like spiders friction/heat and other losses. What's most important though is the voice-coil. Adding power is the BIGGEST, and only TRUE form of RISE that you CAN worry about. As Ed said, for music, you don't want to play with impedance which is correct. However it would be great to keep RESISTANCE down. Resistance is a HUGE part of the total impedance, they are combined together in this value when you are using alot of power. It is sort of static and dosn't really depend on frequency.
When measuring total impedance, it is not all Impedance actually. What can you do to change Resistance? It's caused by adding alot of power to the subwoofer. The more you add, the higher your resistive rise. You can witness a change by measuring at different power levels. Try measuring at 100w vs 2kw. This is why competitors don't gain much by adding stupid amounts of power. This is why subwoofers are truely rated a bit less then what they can take before frying or bottoming out because you are wasting power at a certain point. The amount you can send to a sub before having to worry about rediculous amounts of rise depends on teh size of the motor and coil.