The word for garden in Russian, and also in Belarusian, Ukrainian and Serbian, is сад [sat], which also means orchard. It comes from the Proto-Slavic word *sadъ (plant, garden).
The word for garden in most other Slavic languages is the same: sad in Croatian, Slovenian, Polish, Slovak and Sorbian. There are also similar words in Latvian (sads) and Lithuanian (sõdas) [source].
The word sad also exists in Czech, but just means orchard. The Czech word for garden is zahrada [ˈzaɦrada], which comes from za (for, in, behind), and hrad (castle), from the Proto-Slavic *gȏrdъ* (settlement, enclosed place). So zahrada could be translated as “in/behind the castle” [source].
*The Proto-Slavic *gȏrdъ comes ultimately from the Proto-Indo-European *ǵʰórtos (enclosure), which is also the root of the Irish gort (wheatfield), the Welsh garth (hill, enclosure), the Latin hortus (garden), and the English horticulture, yard and garden, and related words in other languages.