Isomorphic submodules of a filtration

Question

Is it true that $t^{-n}\mathbb C[[t]]$, $n>0$, is isomorphic to $\mathbb C[[t]]$ as an $\mathbb C[[t]]$-module? I think yes, since $t^{-n}\mathbb C[[t]]$ is a free $\mathbb C[[t]]$-module of rank $1$. What makes me uneasy is that the filtration $\mathbb C[[t]]\subset t^{-1}\mathbb C[[t]]\subset\cdots\subset t^{-n}\mathbb C[[t]]\subset\mathbb C((t))$ would then imply that all submodules in the increasing filtration are isomorphic which is confusing.