Actually, it refers to the turret portion, not the socket, per se, in naval parlance.
According to Dictionary.reference.com:
bar·bette P Pronunciation Key (bär-bt)
n.
A platform or mound of earth within a fort from which guns are fired over the parapet.
An armored protective cylinder around a revolving gun turret on a warship.
It's the above deck armored cylinder around the gun mounts, for example on the Monitor or Merrimack. The guns were inside it, and it usually rotates with the guns (though some were deck fixtures...
So, really, it's late age-of-sail early age-of-steam armored deck guns, as opposed to unarmored deck guns. True turrets, in the modern sense go beyond simply armoring a gun; they integrate the gun and armor into a unified whole. modern style turrets appear later, as well.
Keep in mind, the guns of the period were mostly free-rolling artillery placed into tracks, and larger, footed, guns basically "bolted down" to the deck, to keep them from breaking through rails, etc., when the ship listed. Barbettes then begin to protect these, some permanently fixed, some fixed to the rotating carriage; most of these guns were still manually turned. Most of these "Fixed Swivels" sooner or later used below deck magazines.
I know there is specific difference beyond this in the 1880-1912 timeframe, but don't have the references to hand. (stored, most of them.)
The best comparison is that the Traveller turret represents the pintels of a naval craft, like the .50Cal MG, Nordenfelt, and QF2#. Barbettes the smaller artillery, like a BB's 5" 50Cal or a twin 3" secondary. Bays represent 8, 10, and 12"" singles, dual 5's and 6's, and even dual 8"... Spinals represent twin and trip 12's and up...
At least, that's how I see the correspondence.
