On the NCL site, many of the "family" cabins are I4, B4, M4, etc.
NCL actually has many categories within Inside, Balcony, etc. like cruiser2015 linked, but the site hides what the actual category is (IA, IB, I4,...). Not every ship has the same categories.
3rd party travel agent sites are better about splitting them up and showing the true category better.
My understanding is that the "family" category should sleep 4 people and be located near things that might interest families. But other categories can sleep 4 as well.