Here's the quote: “Some electric car motors use the permanent magnet technology, probably the most famous is the Tesla Model 3 Long Range. All the other Tesla models — Model X and Model 3 standard — use induction motors,” said David Merriman, a senior analyst at metals consultancy Roskill.
I think the author meant to say "Model X and Model S." Either way, it would make no sense for Tesla to use different motors for each battery size. I'm almost positive all Model 3 variants will use permanent magnet motors, unless they do something special for the performance version.
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.
I imagine that the performance model might include a large, rear induction motor. I have nothing to base this on, it's just a guess. But if you want to do Ludicrous mode, it seems like a higher power option might be the way to go, even if they even it out with a permanent magnet in front. IDK if combining the two would even work, or be feasible but that's my guess... based on nothing.