Permutation and modes of operation
if a cipher operates on fixed length blocks it has to be a permutation by definition since a one to one function is automatically a permutation on the finite domain $\{0,1\}^n.$

This gives the Electronic Codebook Mode, which uses a key to choose which pseudorandom permutation to use, but it leaks information, so modes of operation were invented for block ciphers, to stop equal messages resulting in equal ciphertexts.

Stream ciphers are not permutations in general. Stream ciphers don't have modes of operation in general.

Permutations play a significant role in asymmetric ciphers as well, and the discrete log map over the multiplicative group $Z_{p}^{\ast}$, for example,  is a permutation.