They do NOT mean exactly the same reason, which is why you will always have both. "Stator" is a mechanical designation while "Field" is an electromagnetic designation. The "Field" is the source of magnetic flux (either a magnet or an electromagnet). The "Stator" is the stationary portion of an electric machine that surrounds the rotor. For brushed DC motors, the terms are often used interchangeably, because the Field resides in the Stator (in the case of series wound brushed DC motors, the field is an electromagnet, so the stator contains field windings. PM brushed DC motors have magnets in the Stator). But in other motors, such as 3 phase AC motors or brushless DC motors, the field resides in the rotor, and the stator contains the armature windings (which are in the rotor in a brushed DC motor).These two sentences mean exactly the same thing
" I need the in-line reactor in series with the stator"
" I need the induction coil in series with the field "
So if you are working with more than one kind of motor, the distinction is very important, so those two terms aren't going anywhere. Sorry it makes your life harder, but motors are complicated beasts.