...there are 2 different points of view: talking about POI in MRA and talking about POI in Navi device.
Different between Favorite and POI in MRA are well explained above: Favorite is only for your own use (kind of data base and can be used as waypoint in your routes. As far i know, it's not downloadable.
POI is also usable as waypoint for your MRA routes, but can me moved together with your route onto your Navi. So you can in your Navi also select just one of that POI as target for navigation - or the whole route as usually.
Also POI can be downloaded as GPX file, to have a Backup, to load onto your Navi or to share with others. This GPX file then will contain only those waypoints, but no route.
If your collection of POI contains for example 10.000 items (may all McDonalds Restaurants) many of Navi devices can't accept the file with more than 50 or 100 POI=waypoints. The trick is, to use website "gpsbabel" to transform this POI GPX file to the file format GPI. In such a format, Garmin Navi will accept also more than 10.000 POI in the file.