Phase current is the current that is flowing through the windings of the motor, and "rated current" is the Chinese term for the battery current, the current drawn from the supply.
Battery current is always lower than, or the same as, the phase current. Phase current can be several times higher than battery current under some conditions.
When we refer to current limits here we're normally talking about battery current ("rated current"). The exception to this general rule is the Kelly range of controllers, where, presumably for marketing hype reasons, they tend to refer to current limits as phase current.
The reason phase current can be higher than battery current at times is down to the way the controller works. It's really a switched mode power converter, like that used in power supplies, so can convert a higher voltage at a lower current into a lower voltage at a higher current. When a motor is running slowly, but under a heavy load, it will have a low voltage across the windings, but will need a high current to generate enough torque. The controller allows this, by converting the battery voltage down to a lower voltage at a higher current.