Windmills grind corn, they don't pump water, wind pumps do that and yes I agree that wind generators produce wind ( But so do beans).
I think that in the last few years when wind power has been taken seriously the term wind turbine has become the accepted one but for the first 50 years of my life they were windmills and I am not likely to change.
In the world where half the stuff is misnamed or named after trade names such as Hoover, Biro or Tannoy to quote three that come to mind, I don't think it matters much as long as the meaning is clear.
Much more confusing is the turbine rotor itself and that may be the best name for it. I use propeller because I have been using it since a boy, I know it ought to be on an aeroplane or boat but at least it is always described by its diameter and that way there is no confusion. Using blades to me is very confusing as I regard 3ft blades as meaning blades 3ft long. On a wind ( whatever we decide to call it) that implies a rotor diameter of 6ft. For a steam or gas turbine with 3 ft blades it could be 20ft diameter.
Flux