The difference is more than just syntax, at least in the case of Java and Rust. The core problem with checked exceptions in Java (as demonstrated in most of the examples from TFA) is that they don't compose properly with generic functions like map. Checked exceptions exist in parallel to the type system, and other parts of the language don't have the capacity to deal with them.
On the other hand, a Result type makes errors part of the type system, and all other code can work with them "by default".