A conductor with a net unbalanced charge, which is then grounded, will acquire whatever charges needed from the ground to become neutral once more.
OTOH: if you induce a separation of charges in a neutral conductor (say, by bringing a charged object close to the conductor) and ground one side of the conductor, then it will be left with an unbalanced charge.
eg. bring a negatively charged sphere close to a neutral conductor to get + charges on the near side and - charges on the opposite. Briefly ground the far side. Remove the sphere. The conductor is now positively charged.