A charge at rest produces:

Electric charge: The property of matter which is responsible for electric and magnetic effects is called electric charge.

Magnetic field: The space or region around the current-carrying wire/moving electric charge or around the magnetic material in which force of magnetism can be experienced by other magnetic material is called a magnetic field/magnetic induction by that material/current.

Electric field: The space or region around the electric charge in which electrostatic force can be experienced by other charged particles is called an electric field by that electric charge.

When a charged particle is at rest then it only creates an electric field around it.

When a charged particle is moving with a constant velocity creates both electric fields as well as the magnetic field around it.

When a charged particle is moving with acceleration then it produced an electromagnetic wave around it.

Electric field and magnetic field are not independent. They are two aspects of the electromagnetic field.

Charge at rest only produces an electric field.

Moving charge with acceleration produces both electric field and magnetic field.