The Model 3 motor is not a straight permanent magnet motor either, by they way. Other EVs like the Leaf, Bolt, etc. use true permanent magnet motors that make use of a large piece of rare-earth material as a magnet. The Model 3's motor is (rumored to be, not confirmed) a permanent-magnet switched reluctance (PMSR) motor. This motor uses a rotor that is mostly iron/steel, with small permanent magnets embedded to smooth out the torque ripple. In terms of the article, this means the Tesla motor uses a lot less of the rare-earth metals than other motors.
However, I don't think there will be any difference in motor between the Model 3 LR and SR models. The only possibility here is that the (eventual) performance Model 3 might have something different.