Electric charge is one of the quantum properties of elementary particles. You have a charged body, if the numbers of positively and negatively charged particles in it are not equal. And it does not have to move to create an electric field.
It is different with the magnetic field. It appears only when a charged object is moving. As motion is always relative, this charged object has to move relative to an "observer" or an object that can detect magnetic field. Imagine two observers. One is motionless, and the other is moving together with a moving charge. The first will observe the magnetic field, the second will not.
How will the motionless observer observe the magnetic field? That field will change, as the charge will be passing by. This will result in appearance of non-conservative electric field, which will interact with charged particles making the body of the observer and will make them move. There will be some changing electric current in the body of the motionless observer. This current will be an indication that something affects the charged particles (electrons and ions) in the body of the observer, and that something is the electric field created by the changing magnetic field created by the charge flying by.
