More specifically, a low voltage (LV) motor is normally <1000 V or <600 V, depending on who you ask. They are usually wound with round enamel-covered wire. This is called random-wound or mush-wound coils. Medium voltage (MV) motors, with voltages up to 13.8 kV or even higher, are wound with rectangular cross-section copper wire with enamel or mica tape insulation, depending on the voltage level. This is known as form-wound coils.
Because form-wound coils must be individually insulated and formed to precise dimensions, it is much more expensive to manufacture. Also, because of the thicker insulation required due to higher voltage levels, a MV motor will normally be larger and more expensive than a LV motor of the same rating.
Depending on the country, industry, and specific user, the philosophy of where to use LV and MV motors is different greatly. The break point is typically somewhere between 200 and 500 HP (or kW), although MV motors are available at lower powers and LV motors at higher powers. The LV motors will draw higher current, so cabling, switchgear, etc., must be sized accordingly. But LV equipment is less expensive than MV gear.
More often than not the higher voltages are bar wound, with rectangular section copper wire, which may have or not an enamel coating and or a half lap or similar tape wound on copper to provide turn to turn and layer to layer insulation. At 5kV and above the insulation must also resist Corona Discharge and this usually means an insulation which contains mica, usually in fine flakes, in a resin to bind it when cold at wire manufacturers. This can be a thermosetting resin or a thermal cure VPI resin, either epoxy or polyester based. The coils when ready for machine mechanical assembly should be in the slot, connected at nose ring, resin coated in VPI and baked in an oven, such that full penetration of resin has occurred in the slot area and no air pockets remain. (Source of discharge to earth causing insulation to breakdown into a white powder and then fail to ground at that spot which has had the insulation degraded to be effectively unable to withstand even running voltages.)
LV machines are usually "mush" wound and being LV there are only 1, 2 or 3 turns per slot and end ring connections are designed to have a connected machine with in any slot a low delta V between wires which can also be quite random in slot location and turn 1 can be in close contact with turn 3, whereas in a MV machine being bar wound the randomness is gone and the highest delta V is restricted to one turn.
Note: All the rotor does is provide a magnetic field of the same flux density whether it is LV or MV.