My grammar book says they both mean ‘if that’s the case...’ but it doesn’t clarify the differences.
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それなら implies that the speaker anticipated multiple possible answers, or didn't anticipate what was just said. It's fundamentally more reactive.
おなかすいたな (I'm hungry) それならご飯にしようか (if that's the case, let's have a lunch)
それでは can be interchangeably used here and when used like that, it sounds a bit more formal than それなら.
In addition, それでは is also used in the context where the speaker is actively suggesting/driving a topic.
それでは試験を始めます (we shall begin the exam)