Did you maybe mean "the checked type"? In that case I still think it's not equivalent because at least in Rust you can automatically transform the error while it bubbles up, while I don't know of a language with checked exceptions that lets you transform the exception while unwinding (short of manually catching, transforming, and re-throwing).
As far as I know, that's how Java's "throws" method signature works, which has been widely regarded as a mistake.