No, it is not true that an electric current can only flow if two objects have a different charge. In fact, an electric current can flow even if there is no charge difference between two objects. This is because an electric current is simply the movement of charged particles, and it can occur as long as there is a path of low resistance for the charged particles to move through.

For example, if you connect a battery to a light bulb, an electric current will flow from the battery to the light bulb even if both objects have the same charge. This is because the battery provides a path of low resistance for the charged particles to move through, and the potential difference between the battery terminals causes the charged particles to move.

In general, an electric current will flow whenever there is a difference in electrical potential between two points, regardless of whether or not the objects at those points have a different charge.