What is the difference between a permutation and a shuffle (transposition cipher)
A shuffle (or transposition function) re-arranges elements of the input. A permutation re-arranges the entire output domain.
For example, compare the following transposition function and pseudorandom permutation:
The transposition takes in a 4-digit number, and re-arranges the digits. 1234 might become 4213, but never 1692.
A pseudorandom permutation has a shuffled list of all possible 4-digit numbers, and an unshuffled list of all possible 4-digit numbers. It looks up the input number in the unshuffled list, finds the corresponding number in the shuffled list, and outputs that. 1234 might become 1692.