Sawagakuresato literally translates to the “Swamp (Sawa) Hidden (Gakure) Village (Sato)”. It’s full title is in fact 死沢隠れ里 or “Shizawagakuresato”.
As with many Japanese terms, it is often shortened in informal speech. Then the decision of how much or this proper noun is handled differently by different translators. That’s why you hear about “The Sawa”, “Sawagakure”, The Hidden Swamp, and any number of variances. In fact, the swamp in this story is called “Shizawa” or “Death Swamp”, so “Hidden Death” or “Death Swamp Village” might show up. It’s all the same place. It’s your home.