The Concierge Lounge and the Diamond Lounge are two separate places.
The Concierge Lounge is for guests in Grand Suite and higher category accommodations, regardless of their Crown and Anchor level, and also for Diamond Plus and Pinnacle Club members no matter what cabin they are in.
The Diamond Lounge is for Diamond, Diamond Plus, and Pinnacle Club members no matter what cabin they are in.
Guests in Grand Suites or higher categories who are not Diamond, Diamond Plus, or Pinnacle Club are not allowed to use the Diamond Lounge. They can only use the Concierge Lounge.
Guests in Grand Suites or higher categories who are also Diamond Members can use both lounges, and both concierges.
Royal Caribbean is trying to make the Diamond Lounges as close as possible to the Concierge Lounges as far as amenities but there are some differences that will favor those in Grand Suites or higher. For example, on the Oasis class ships, you can order a hot breakfast and also lunch in the Concierge Lounge but not in the Diamond Lounge.
I don't know if the Brilliance Concierge Lounge offers the menu service.
Generally, the expectation is if you are in a suite that rates the Concierge Lounge you should use it, and that concierge, no matter if you are a diamond member, since this frees up space in the diamond lounge for upper level members who are not in suites. The diamond lounge can get overcrowded very easily and so when we are in a Grand Suite we stick to the Concierge Lounge. It might help if they renamed it the 'Suite Lounge' or something like that in order to cut down on confusion.
Frankly I expect the company to kick diamond plus members out of the concierge lounge once they have retrofitted diamond lounges on all the ships. There are simply too many diamond and diamond plus members to manage.