Hi there, both are really family staterooms in that they can sleep at least 4. The regular stateroom w/veranda sleeps 4 and has a standard tub/shower. The "deluxe" family stateroom w/veranda can sleep 5 and have a round shower/tub with a rainfall shower head.
If your party has 5 people, there will be a Murphy bed near the veranda door. If you have less than that they will just have an extra chair in that spot.
We travel just as a couple, we alternate between the 2. I'm a fan of the round shower in the family one and it does have just a little more space. If I've got the little extra $ to spend we do the family, if not we do the other.
And yes, the categories are related to type of room and location. There are other options you can pick such as a deluxe stateroom with extended, undersized, or navigators veranda. Then of course the ocean view rooms that just have a porthole and then the interior rooms.