Question about high current amps versus "not high current amps"

Those are formulas for static case, i.e. single wave. But is amp capable of delivering a lot of current on high transients QUICKLY? It may be high current capable when single is stable, but what about transitions (which is what music is)? Is it able to raise current and provide energy fast enough?

Thank you to @everybody for the great feedback!!!!

I am going to try to simplify what I think I got out of the answers that were generously provided, and see if I've got it:

C WPC are a product of the voltage that the power supply supplies x the current.  The amp could be rated at a certain amount of WPC but if the current dropped off whenever it (the amp) encountered a significant drop in impedance then the amount of wpc that it was theoretically rated as putting out would also drop way below what it was rated at?  Unlike a "high current amp" in which the current would not drop so therefore the wpc would remain constant?

(So would this mean that the rated wpc is almost meaningless if the current isn't enough to sustain that wpc?)

So if I have that right, does the 4 ohm tap have any bearing at all on whether the amp is a high or low current amp?

And would there be a specification listed that would tell me how an amp stacks up as far as the amount of current?

Again, thanks for all the input, it is greatly appreciated!  

Excellent and informative discussion. Thanks to all even if it is a bit tough for dummies like me to understand

How does any of this inform a future purchasing decision or help us enjoy what we have now?

Amplifiers are not about power. Power is consumed by the load, whether it's a resistor, a motor or a speaker driver. The amplifier is an energy source and does not necessarily follow Ohm's Law. As an example, if you short a 9-volt battery with a 1/2-ohm resistor, Ohm's Law dutifully informs us that the "power" delivered is 162 watts (9Vx9V/0.5) and the current is 18 amps. Of course that is ridiculous; the energy storage of a 9V battery is limited to about 500 milliamps and only when a resistor limits the battery to less than 500mA does Ohm's Law apply. On the other hand, that 150kVA utility transformer feeding your street can easily slam thousands of amps over a bolted fault. It's all about energy.

An amplifier has an energy source: the power supply's transformer and filter capacitors. If the power supply can maintain it's secondary voltage from any load the speaker presents it, you can call it a "high current amplifier" and relationships established by Ohm's Law apply. But if the output voltage sags when the speaker load drops, then the current delivered to the speaker will decrease, which means the power consumption decreases.

If an amplifier's specs says it can maintain voltage down to 4 and/or 2 ohms, you will see the power double (i.e. 100W into 8 ohms, 200W into 4 ohms and 400W into 2 ohms) and that is practically a true voltage source. But if you see 100W into 8 ohms and 150W into 4 ohms, then that amplifier is not as good of an energy source.