Barb unarmoured defence is an AC calculation method. It calculates your AC as being "10 + Dex Mod + Con Mod"
Mage Armour also supplies an AC calculation method. It calculates your AC as being "13 + Dex Mod"
If you were a multiclass monk you'd have Unarmoured Defence (Monk) as well, which would give you a third method of calculating your AC - "10 + Dex Mod + Wis Mod"
Draconic Sorcerer gets one too - "13 + Dex Mod"
Each of these methods of calculating your AC are as stated - you calculate that specific way. You can choose which AC caculation method to use, but you only use one - in game terms, it picks picks this for you, and uses whichever one provides the highest overall AC. If a class feature, item or ability simply lets you add something else to your AC, it says so; Shields, for example, add their AC bonus to your existing AC calculation, rather than describing a new calculation method.
Larian is horrendously bad at giving accurate information with their tooltips, unfortunately, and often leave misleading phrases and descriptions in place. There was time, early on, when the tooltip for mage armour just said it added 3 to your AC, for example, which was always incorrect - just lazy.
At this point the game seems to be handling AC more or less correctly, with the exception that it always counts your shield, whether you're wielding it or not, which is (hopefully) a bug.
