For Gravity:
If you want the honest answer to what causes it, scientists have no idea what actually cause gravity. Theoretically speaking scientists believe their is particles called “Gravitrons” which are responsible for gravity itself. We know the relationship between our universe and gravity, however we’ve never seen the force in action.
For Magnets:
Their a force called electromagnetic attraction, which is essentially the “need to want to shift your energy so it’s balanced” and as such positively charged ions are attracting negatively charged particles. The resulting effect is then what causes for the pull in magnetism between A to B.
They don’t really have any relationship because they are two totally distinct fundamental forces.
Gravity is a property of all matter. Everything that has mass is attracted to everything else that has mass, and we don’t really know why beyond the observation that this seems to be a fundamental property of space-time. So far as we can tell gravity is always attractive and never repulsive – i.e. there is no “negative gravity” – though certain physics equations would still work with repulsive gravity, it would imply objects with negative mass, which we’ve never encountered. Gravity is also extremely weak compared to all other fundamental forces.
Magnetism on the other hand arises due to the electromagnetic force. Some particles have a property that we call charge, which can be either positive or negative. This property causes particles of opposite charge to attract one another, and particles of like charges to repel one another. Again, this seems to be a fundamental property of the universe: it’s just one of the fundamental interactions that the particles that make up our universe can have. Most matter is made up of both particles of negative and positive charge, but some arrangements of matter have particular geometric arrangements of these particles in them that causes them all to line up. This is what a magnet is: because the electromagnetic forces in all the individual atoms in the material happen to be aligned, you get a magnetic attraction/repulsion on a much larger scale.
Gravity has a rotational component to it, it’s not just attraction. A spinning perfect sphere cause things to move along its direction of spin.
Same goes for electromagnetism. A spinning charged perfect sphere cause opposite charge objects to move along its direction of spin.
We typically split electromagnetic force into 2 components in daily life: the rotational component, and the attractive component; the rotational component is the magnetic force. However, we don’t do that for gravity normally, and in fact we didn’t know that is possible until general relativity (Newton’s theory will only give attractive force). The rotational component of gravity is called gravitomagnetism.
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