Nominal torque is usually on some nominal rotation speed, which should be mentioned too.
Maximal torque is usually on zero speed (or even more if you force it to rotate backwards). And the maximal current is usually a lot higher than the nominal on nominal speed and torque.
So it says, that if your motor is running at nominal, it would take the 380mA. You can safely assume, that at many occassions, even in normal usage, the current will be temporary a lot higher.
Power supplies usually state how much current they can provide for a long time (nominal current); good power supplies also state maximal current and how long it can provide it (might also be called surge current).
I personally would consider the 500mA highly underrated for full usage of the motor, but if the power supply is over-current resistant (be it by detection and sophisticated construction, or be it just "weak" source with high inside resistance), then it may work well enough, just sometimes the motor would seem "weak" as the voltage would need to drop in order to keep step with current provided by source. And low voltage means low current means low torque there. On some application it dos not matter, it would just move slower, on other applications that may be a critical flaw - it is you, who decides, what is acceptable and what not.