Understand Python swapping: why is a, b = b, a not always equivalent to b, a = a, b?

From python.org

Assignment of an object to a target list, optionally enclosed in parentheses or square brackets, is recursively defined as follows.

...

• Else: The object must be an iterable with the same number of items as there are targets in the target list, and the items are assigned, from left to right, to the corresponding targets.

So I interpret that to mean that your assignment

nums[i], nums[nums[i]-1] = nums[nums[i]-1], nums[i]

is roughly equivalent to

tmp = nums[nums[i]-1], nums[i]
nums[i] = tmp[0]
nums[nums[i] - 1] = tmp[1]

(with better error-checking, of course)

whereas the other

nums[nums[i]-1], nums[i] = nums[i], nums[nums[i]-1]

is like

tmp = nums[i], nums[nums[i]-1]
nums[nums[i] - 1] = tmp[0]
nums[i] = tmp[1]

So the right-hand side is evaluated first in both cases. But then the two pieces of the left-hand side are evaluated in order, and the assignments are done immediately after evaluation. Crucially, this means that the second term on the left-hand side is only evaluated after the first assignment is already done. So if you update nums[i] first, then the nums[nums[i] - 1] refers to a different index than if you update nums[i] second.