The motor rating isn't just the maximum power it should survive.
And there is no certainty that the label shown lists the maximum power the motor should sustain, or avoid, or whatever. There is no enforced standard.
But labeling the power rating as 'Maximum' does suggest someone is saying this motor has 'Maximum output' of 1000w. That might be shaft horsepower, or it might be maximum sustained electric power before the motor is damaged, etc.
Most '250w' motors will sustain 1000w+ electric power on steep hills or other loads - but only for a short time. The somewhat standard legal rating of these motors for bicycle use means something like "if the motor is sustaining more then 250w for more than 5 minutes, it's rated higher than 250w". But if the motor can sustain power of 250w for longer than 5 minutes, but fails after 5 minutes of more than 250w, then it's legally rated at '250w'. The different laws specify different ways to measure whether a motor meets it's rating or not - some laws don't even specify how to check.
The most common legal rating of motor power is - "what can it sustain without burning out?". My 250w (or 350w) rated ShengYi SX2 routinely displayed 1000w+ on 12 degree hills, but the motor temperature was rising, and something would melt if I kept that up for very long.
So, who wrote that label, what did
they intend for this value to mean, is it guaranteed, is it a reference to a legal standard? Can't tell by that label alone. From what you write, I'd infer this is intended to be a '500w' motor (which would mean it can pass 500w of power all day without burning out), and is expected to handle 1000w of power for short periods - but by what definition of 'short', we don't know. By what standard of precison, etc., who knows?
And, yes, electric motors are like that.
