Tamely ramified extension of local fields

Question

I am trying to understand the tamely ramified extensions of a local field. First of all, when would be two such extensions $L_1/K$ and $L_2/K$ over the same base field be isomorphic? Second, for totally ramified extensions of local fields $L/K,$ there is a result that says the extension can be written as a tower of of extensions $K \subset K^{\textrm ur} \subset L$ where $K^{\textrm ur}$ is the maximal unramified extension of $K$. Is there a similar result for tamely ramified? (i.e., a totally ramified extension $L/K$ with an intermediate field, say $T$, such that $T/K$ is the maximal tamely ramified)? If there is, would $T$ be unique?