Magnetism, it has been derived, is a consequence of the combination of the electrostatic force and special relativity. I don't have the derivations handy, but if you have two electric charges moving with respect to each-other, they will exert forces in addition to their at-rest electrostatic forces, and these additional electrical fields are what is described by magnetism. From a quantum-mechanics prospective, the electromagnetic force is mediated by the exchange of virtual photons, although how exactly this exerts an attractive force is beyond me (I can easily see it creating a repulsive force, but not attractive). Nonetheless, it does, as we know from common experience.
Gravity is different. Gravitation occurs when the presence of mass or energy curves the fabric of space-time, causing points of space to draw in towards the source of the gravitational field. Objects in such a field simply follow their path in space-time, which means they are drawn in the direction of nearby masses. We normally observe these interactions as a force, but within the frame of reference an object in free-fall, there is no obvious force that is at work, because gravity affects all objects in proportion to their inertia.
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