I've done some research and spent more time thinking about this. Provide feedback if any of this is inaccurate.
Basically, magnets get their magnetism from the magnetic fields of all of the atoms lined up together. The magnetic field is generated by the motion of the electrons in the atom itself and with a sufficiently amount of atoms (e.g. quadrillions) that have non-cancelled out electrons and non-cancelled out fields it adds up to a measurable magnetic field. After thinking about it a lot, I concluded there is no current because:
- There is no closed loop. Consider an iron bar magnet, it has a north pole and south pole. While outer electrons in iron can move freely, there is no circuit and hence no current.
- While magnetism is the result of energy (moving electrons), in a magnet, there is not enough energy to be shared with another body because the magnet is at a state of equilibrium.
Consider the example where I connected the 2 ends of the bar magnet with a wire? While outer electrons in iron could move between atoms, the electrons would not move across the wire because they are stable within the iron solid. Electrons won't just jump from the bar magnet to the circuit. This would require work, something to push the electrons; otherwise they are happy to keep orbiting the atoms of the magnet.
In a battery, chemical reactions "push" electrons from a negative side to a positive side through a circuit.
In electromagnetic induction, kinetic energy from moving coils in a magnetic field is used to generate electricity by "pushing" electrons within a coil across a circuit, they don't just spontaneously push themselves because they are connected to something that they can share electrons with.
As an example, imagine connecting a bunch of gears together. Just because they are touching doesn't mean they just start making each other spin. Something has to start making them spin.