What is the difference between electric field and electrostatic field?

The main difference is that Electrostatic field is because of a stationary charge. And Induced field is because of a changing magnetic field. Since magnetic field and electric field are the same thing in different frames of reference.

Semantically? An electric field does not have to be static while in electrostatics it's generally assumed that the electric field does not change or only changes so slowly that its rate of change doesn't matter. That's very different in electrodynamics where electric and magnetic field changes are always coupled.