Reminder: how to tell current from an amp's specs?

Simple. I'm thinking about getting a new amp for my Maggies. A number of people recommend a high-current amp for them. (Some say this is a myth.) The repeated line is: "it's not the watts; it's the current." So I'm curious how people determine which amps have high current. It's that simple. I don't need a number and I don't mean to suggest that it would determine which direction I go in. It just makes me curious how people know if an amp is high current or not. (Let me add that I'm not trying to open a debate about Maggies with tubes or Class D or anything like that.)

I'll add as well that I'm a humanities professor, not an electrical engineer. I don't even understand what people mean by "power" out here (In cultural studies, we use that term in a Foucauldian sense.) Sometimes that word seems to mean watts, sometimes current, or voltage, or ....  I once set up a model train for my son. It took enormous focus for me to work through these terms, and unfortunately what little I learned is gone.

I may be completely wrong, but I've been under the impression that an amp was considered "high current" if it was able to double (or nearly so) it's output wattage every time the load resistance was halved. So, 50W into 8ohms, 100W into 4ohms, 200W into 2ohms. Many amps won't do this, some will.

Thanks to everyone! And @atmasphere , I wrote my response before seeing that you had posted your very helpful response. I think I'm getting it!

Ohm’s law alone does not apply to power. If you put a 4-ohm resistor across a 9-volt battery, does that mean the resistor is consuming (9*9/4) 20 watts? No. That would mean the battery would have to accommodate the resistor with slightly more than 2 amps, but it the most it can do about half an amp. So the answer is a high current amplifier is one where it stores enough energy to maintain voltage over the speaker’s varying impedance.

You cannot tell from the specs how much energy it stores because most of the manufacturers specify the power at only one impedance (an 8-ohm resistive load). A speaker presents an inductive load which varies with frequency. But you can get an indication of the performance if the manufacturer provides power ratings at less than 8-ohms. Levinson, Krell and the like maintain their voltage (energy) down to two ohms. If an amp can do that at a 1-ohm load, then it’s truly a high current amplifier. Literally.

Here is another well-written article on this topic:

http://education.lenardaudio.com/en/14_valve_amps_7.html