How to tell the current from the amp

A good indication of a high current amp is how large and well built the power supply is.

Dragoncave. There is no one answer that is going to give you the magic number. Welcome to audio. It's a complex topic. Experience helps. There are guys that think a 200 buck amp is going to deliver the same performance as a high end amp at multiple dollars more. That's just pure fantasy, just like everything else you buy, quality costs money.

I get the case where you have double the wattage with half the impedance, but such case only show the device is qualified as high current, but now by how high as a quantifiable measurement. It’s only a relative measurement. So there is no one measurement available to indicate the “current” capability? I don’t have electrical technical back, and I feel this concept is being mystified…

Measure the voltage.
The equation V=IR can be refactored to be I = V/R.

Once you have V and the impedance plot, then you know R at any, and all, frequencies.

If it is a constant 8 ohms, then I=V/8.
If it is 2 ohms, the I=V/2
If it varies with frequency, then it gets harder.

There is not a lot more to it than ^that^.

If the amp it trying to hit 50V, but only have rails at 28V, then you run out of voltage.
If the impedance that you are trying to drive is low, and the power supply has little capacitance and undersized in the transformer, then you cannot maintain the “umph” for very long.

If you are concerned with current, then you likely have a speaker than is very low impedance, or maybe have been told that you should be looking for current specs as a way to determine which amp to use.

I will just add that amplifiers with FET's typically have a higher current rating than bi-polar devices. This also yields to a high slew-rate which helps with transient peaks. I've not seen tube amplifiers that can match current capabilities of SS FET amplifiers.