Confusion with the nameplate of an induction motor
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Two connection methods.

The windings on your motor can take 220 V between their terminals. 


On a 220 V 3-phase supply you connect as shown in Figure 1b.
On a 380 V 3-phase supply you connect as shown in Figure 1a.


Note that in each case the voltage across each winding is 220 V while the voltage between the supply terminals may not be.

It is simple trigonometry to show that the 380 V phase to phase voltage is \$ \sqrt 3 V_{p-n} \$.