If we encrypt a message $m$ with (say) $AES$ and key $k$ we get ciphertext $c$. And if we encrypt the same message $m$ but with $k^*$ we get ciphertext $c^*$:
1) $AES[E_k(m)] = c$ and $AES[E_{k^*}(m)] = c^*$
But what if we were to tweak $AES$ insted of changing the key? For example, a simple tweak might be to change the ShiftRow from right shifts of $0,1,2,3$ to (say) right shifts of $1,3,0,2$. And perhaps unique shifts for each round of the $10$ rounds.
Then, if we encrypt a message $m$ with (say) $AES_{tweak1}$ and key $k$ we get ciphertext $C$. And if we encrypt the same message $m$ with $AES_{tweak2}$ and with the same key $k$, we get ciphertext $C^*$:
2) $AES_{tweak1}[E_k(m)] = C$ and $AES_{tweak2}[E_{k}(m)] = C^*$
Since these ciphertexts in (2) are distinct is this the same or similar to changing the key, as in case (1)?
Let's assume sender and receiver can secretly exchange the tweaks.