Here it is in easy terms in a nutshell. All wattage does is move the speaker, it does that by creating an magnetic field around the voicecoil that the electricity flows through. The overall force that moves the speaker however, is made up of 2 fields that either repel (cone moves out) or attract (cone moves in). Speakers are powered by ac because the current moving each direction makes the field change directions. The second field, however is static, that field is created by the magnet on the back of the speaker. It's the total force of both that moves a speaker. So "motor force" is the strength of the field created by the permanent magnet. The second field around the coil gets stronger as more current flows through the coil. That's why speakers move further when you put more power on them, the force the coil is contributing gets stronger. So a strong motor, like on most expensive speakers, tends to be stronger than what's on most low end speakers, hence they tend to have more bass on a watt/watt basis.
Lastly, the closer you get to a speakers RMS, the closer you get to being capable of doing damage to the speaker thermally AND the closer you get to power compression, which most speakers have already entered by the time they hit their RMS power levels. That occurs when the coil gets hot, the impedence rises, which drops the current flowing through the coil, remember from above, the current is what adds force to the alternating magnetic field. So at that point, you can begin to see dimishing gains by adding more power, that's why when SPL competitors go from 3000 to 6000 watts they don't gain 3db's. Most of power gets converted to heat, the coil cant' dissipate that much heat, coil heats up, impedance jumps and your getting field strength barely increases, hence the .5db gain lol.