A lot depends on the amp. It's RMS out to Impedance will most likely be logorithmic, not linear. On average, 8 ohms will see 33-66% of what a 4 ohm speaker sees. 37 is probably close, but there is a chance of variance.
That sounds like a generalization, judging from real world experience...
Some amps have an ohm switch - For instance, my 100watt tube amp doesn't turn into a 25watt head when i use a 16ohm cab on the 16ohm setting, and it sure as hell isn't 400watts @ 4ohms - if it's matched it should stay the same
My Peavey Bandit goes from 80watts at 8 ohms to 100watts at 4ohms.
I know in car audio they have all sorts of factors. They will list it as 100w but it is really rated at 50w RMS and the 100w is peak power. Does this apply to music gear as well?
I've noticed that with car audio..they like to tell you the peak output/input for some reason. My experience with musical equipment has been that unless its something off-brand or special design, the RMS output is usually whats given.
Car audio values are usually listed in PEP rating (very short spikes of power surges), professional audio and musician/home stereo is normally rated in RMS (Root Mean Squared) power, or the amount of power it can sustain continuously.
Watts are the product of the voltage and the amperage. With a speaker load, watts are calculated by impedance x amperage^2 or voltage^2 / impedance. How many watts are produced per impedance load depends on what kind of voltage and amperage numbers your amp produces. Tube guitar amplifiers use different taps off a transformer to provide RMS power for whatever speaker load you connect them to.