Noise problem with Arduino + relay + motor unit
Yes, they still need to share common ground.  Exceptions are when optical couplers are used.  But this is usually an extreme case where ground loops need to be avoided or isolation from a dangerous power level is required.

Note, mitigating noise at the source is usually the best option.  In this case are you using a flyback diode across your relay's coil to suppress or eliminate flyback current from the coil's inductor characteristics?  Or placing capacitors across your motor as discussed in this stackexchange.com question / answer to suppress noise from the motor?