This is intentional. Both effects change the way your AC is calculated, and this wording is used in other effects. For example, Mage Armor causes your AC to be calculated as 13 + your Dex modifier, plate mail sets your AC to 18 (with no Dex bonus) and a breastplate makes your AC 14 + Dex modifier (max +2).
All of these effects are mutually exclusive for balance purposes, making a divide between effects that provide a bonus to AC (using a shield, Bracers of Defense, ect.), and effects that change how your AC is calculated. This would prevent you from using both even if the multiclassing rules didn't explicitly prevent you from gaining multiple instances of Unarmored Defense (hence making it so you cannot switch between the two versions of the same ability).