If you imagine a set as a bag of things, then a permutation is one possible result of pulling random things out the bag one at a time and putting them in a row until the bag is empty. What you describe are usually called the n-tuples of a set (specifically ones where n is equal the size of the set). There's some more info here: https://en.wikipedia.org/wiki/Permutation#Permutations_with_repetition

Why do we assume, that ab only results into ab, ba, and not in aa, bb, ab, ba ? Isn't that a true permutation?