One is an imperative gradual opt-in superset of JavaScript, the other is a strictly typed functional programming language with a fairly opinionated runtime.

This defines what they are, but not what use cases they serve. From what I see of the comments and understanding of both TS and Elm, they have use case overlaps.

A hammer and an axe have use case overlaps too. Just because you can build front end apps with both doesn't mean that they serve similar use cases. Elm is more of a framework.