I’m not sure about actual functional definitions, but I think of it based on the size of the various cities involved. Metro seems to be used when referring to relatively large cities and towns that have blurred together to the point you move between them without distinct separation. Whereas Greater is applied when there is still a more clear separation between the core “big city” and the suburban towns around it.
I’ve used most of the options for this and regardless of the tool I do a terrible job of actually coming back and reading anything in them. Instapaper would probably be my vote for the one I used the most though, connected to my kindle it was nice when I used to travel and could catch up on stuff on the plane. These days I use Inoreader for consuming feeds and it also has a good read later function.