Their meaning is expanded through a quantum view, but classically: The total electric flux through any closed surface equals the net charge inside divide by the permittivity. The net magnetic flux through a closed surface is zero (magnetic fields are essentially found as dipoles of North and South; monopoles have not yet been detected). A changing magnetic field induces a propagating electric field, whereas a changing electric field induces a magnetic field (hence when you have moving charges, current, you have a magnetic field---when reviewing displacement currents, note that they tell that a magnetic field is induced that is continuous to that of the conventional current).
One of the points of Maxwell's equations is to show the symmetry between electricity and magnetism...hence you have two concepts of the same phenomenon: electromagnetism