What is the basic difference between electromagnetic fields, electromagnetic waves and constant electromagnetic fields?
An electromagnetic field is generated by some distribution of charges and currents. The electric field tells you what force would be exerted on a “test charge” at a point in space and time. The magnetic field tells you what force would be exerted on a moving test charge at a point in space and time. This is, to my understanding, what fields in general in classical physics tell you.
An electromagnetic field can be constant in all space and time (take for example the electric field given by an electric point charge in electrostatics). This is just a special case of what an electromagnetic field can be. It is not an entirely separate concept from an electromagnetic field generally.
An electromagnetic wave is a disturbance in the electromagnetic field. It is a “traveling change in the electric and magnetic field” that satisfies both the wave equation and Maxwell's equations. Electromagnetic waves are different than mechanical waves traveling down a rope (for example) because electromagnetic waves do not propagate through a medium. They propagate “in” the electromagnetic fields.