They are not different. Electromagnetism is the only thing that exists.
Many have already discussed how one can create another, so I’ll only point out one significant result of special relativity.
Space and time will be divided in different ways by observers moving in relation to each other. One observer will perceive some space as time, while the other will see some as space. This mixing can be seen in the Lorentz transformations.
There is a similar relationship between electricity and magnetism. Different observers, moving in different directions relative to each other, will determine what is electric and magnetic differently. This can be quantified using the Lorentz transformations.
The lesson is the exact same in both instances. Spacetime is the only thing that exists. The same goes for electricity and magnetism. There is only electromagnetism.
Reflecting, I realize that you can get magnetism via electrostatics by using the field transformation properties. It is incorrect. It’s not difficult to see that a pure electromagnetic field cannot be seen in the same frame as a pure magnet field. The whole thing is a fundamental beast.