The difference is only visual, thus also functional, since the interaction is different ;-)

Both act on *-* references and are able to read and write on this type of association.

When to use which; fully depending on the functional requirement. The input reference set selector can only display a single attribute and multiple referenced objects are displayed using a ',' While the reference set selector appears as a list and thus multiple values can be displayed. So the choice when to use which is not a technical, but a functional (UX) decision

PS. since you are posting a lot of questions, its appriciated that you also publish your community profile ;-)

https://docs.mendix.com/community/tools/how-to-set-up-your-profile

PLease take a look at the docs. Here you can read how both, Input reference set selector and reference set selector, are working. 

https://docs.mendix.com/refguide/input-widgets

I think the 'input' refers to the fact that it looks like an input field. In terms of functionality they don't differ at all. Data is being retrieved in exactly the same way.

To me the regular reference set selector is better, because it is clearer in terms of how to add and remove assocations and it also has a search bar (if needed).

Ps. Why is it called Input reference set selector? How can I (intuitively) understand (and thus easily remember) the 'input' part?