Difference between charging by conduction vs charging by induction?

  Charging by conduction requires contact between two objects. Charge is transferred directly from one object onto the other. Charging by induction is done without contact and solely by causing charges to move about in one object by the electric and magnetic fields produced in the other object.

Charges are always repelled by the same charge and attracted to the opposite. If you have a positively charged rod then it will attract negative charges to the closest point on the other rod. If you provide that rod with a ready source of charge such as your hand then it will become overall negatively charged. Take away your hand and it will remain negatively charged even after the positive rod is removed because the charge can't get away. This is inductive charging at its simplest.

If you had touched the positively charged rod to the other rod then charge would have flowed and it would have gained a positive charge by conduction.