What's the meaning of current rating of BLDC motor and it's relation to a phase peak and RMS current?
Who knows what the REX30 specs mean. Basically if you buy this motor, you get what you get. Take a look at the max current rating for the top motor (the 2700 rpm version). The units given are kW. I don't think it actually is intended to be current at all. I think it is power in kW at max current or something. But the range is from 8 to 20.

The seller is not doing a good job of providing the needed engineering data for this motor. It doesn't even say how many pole pairs there are. I guess you have to count them yourself.

But it does give the Kv (64 RPM/V). So we can calculate Kt.

Kt = 60 / (Kv * 2 * pi)

So the Kt is 0.15 N-m/A. So if you know how much torque you need, you can figure out how much armature current will be required to achieve it. The Kv will give you a rough estimate of how much voltage is required to achieve a specific speed, but you would also need to know the winding resistance and output torque to get a real estimate.

As far as the maximum current goes, you can make some guesses. The output power seems to be somewhere between 8 and 20 kW at 2700 RPM. Note, I am making an assumption that the power ratings are for a motor speed of 2700 rpm. If not, then everything that follows will be wrong.

At 2700 RPM, 8kW requires 28.3 N-m.
And 20kW requires 70.7 N-m.
This is based on output power = torque * speed, where power is Watts, torque is N-m and speed is rad/sec.

So at 8kW, the armature current would be 28.3 N-m / 0.15 A/N-m = 190 A.
And at 20kW, it would be 70.7/0.15 = 474 A.

I will run through the calculations for the NT Power motor. But I am not sure they match with the graphs. From the data table, the Kv is 38.5 rpm/Volt, so Kt is 0.248 N-m/A.

Max torque is listed as 61 N-m. So armature current at max torque would be 61 / 0.0248 = 246A.

If we assume max power of 15kW occurs at max torque of 61 N-m, then speed would be 15000/61=246 rad/sec.

246 rad/sec = 2350 rpm.

So according to these calculations, unless I made a mistake, the motor should be able to put out 15 kW at 2350 rpm with 246 A of armature current. The back EMF would be 61 V. The voltage required to supply 246 A would be substantially higher than just the back EMF, because it would have to overcome the winding resistance.

What exactly is the max current specification in general? I don't think there is a single accepted definition. You have to be familiar with motor theory and examine the data from the manufacturer, and if there is any doubt, ask the manufacturer. But I will tell you what max current SHOULD be. Max current should be the maximum armature current that the motor can handle without over-heating. If Kt is known, the max current can be used to calculate the max torque also. Obviously there is an assumption that torque = Kt * Ia, which is only true when the motor is being controlled properly. (Kt is the torque constant and Ia is armature current).

In some cases, max current may be max DC current (from battery or DC bus) and this may be essentially the same as armature current if the DC voltage is well matched to the motor operating speed.

Hope that helps.