Other languages use term "reference" for storing things "by reference" or just referencing any object anywhere in general. It's not like that in Rust.
What Rust calls "reference" is a much more specific thing, that is no so general-purpose. It has a narrower, restrictive usage. Rust references are more like read-only or write-exclusive locks. They make their target unmovable and immutable for entire duration of their existence. They can't exist on their own, only as a counterpart of an owned value.
References in structs also make the whole struct itself temporary, and everything that touches that struct becomes temporary and tied to the scope of the borrowed value that started it.
If these restrictions (that cause you fight with the borrow checker) aren't what you want to achieve, then you don't want temporary references.
99% of the time when you need to store something "by reference", Box (or Arc or String or PathBuf or Vec or some other owned type) is the right answer.
Note that &T and Box<T> have identical representation in memory — a pointer. They differ by ownership.