It is actually quite simple.
It the nameplate states Δ/Y 220/380 this means that this motor is designed and can be connected in delta, if the line voltage is 220 volts. If the line voltage is 380 V then the motor can be connected in star.
This comes from the fact, that the the max allowed voltage per motor winding is 220 volts. In either case the the winding gets 220 volts supply. By connecting this type a motor in delta with line voltage 380 will burn the motor!
When the line voltage is 380V and you want to connected it to delta then the motor nameplate should state Δ/Y 380/660.