Moving electric charges will interact with both electric and magnetic fields. Electric fields exert forces on charges regardless of whether or not they're moving. However, magnetic fields only interact with moving charges.
The interaction of a magnetic field on a moving charge is defined by the Lorentz Force Law. This equation shows that the force due to a magnetic field is proportional to the strength of the magnetic field, the amount of charge and the velocity of the charge. If the charge is not moving and velocity is zero, then the force on the charge due to the magnetic field must also be zero. In contrast, the force on a charge due to an electric field is only proportional to the strength of the electric field and the amount of charge.