Are any two $\ell$-adic Tate twists (non-canonically) isomorphic?

Question

Recall that for a prime $\ell$, the $\ell$-adic Tate twist is defined by $$\mathbb Z_{\ell}(n) := \varprojlim_r \mu_{\ell^r}^{\otimes n}.$$ As abelian groups, we have a (non-canonical) isomorphism $\mu_{\ell^r}^{\otimes n} \simeq Z/\ell^r$. Does this imply that all the Tate twists $\mathbb Z_{\ell}(n)$ are (non-canonically) isomorphic?