I see what you mean. I was trying to use general terms.
The proper wording, for the USN, would be:
Turret - built into the ship, includes a stalk below the weather deck and a barbette.
Mount - not part of the ship's structure. Does not include a barbette.
Triple/Twin - All guns in the turret/mount share a slide or cradle and cannot elevate independently.
Three-Gun/Two-Gun - Guns in the turret/mount are individually sleeved and can elevate independently of each other.
Only the USN apparently had such designations to differentiate the layout. According to Navweaps.com the 135mm/45 Model 1937 and 1938 came in Two-Gun and Three-Gun turrets for the Capitani Romani and Andrea Doria respectively. Navweaps generally uses the USN nomenclature to show what type of turret/mount the other nations used.
So technically, I was half-correct by saying triple turret.