The Russian word for table (the piece of furniture) is стол (/stol/) which sounds a bit like stool in English. In most other Slavic languages the words for table are simliar: стол (Belarusian), stol (Croatian), stůl (Czech), stolŭ (Old Church Slavonic = throne, seat), stół (Polish), сто (Serbian), stôl (Slovak) and стіл (Ukrainian). Although in Bulgarian and Macedonian стол means chair and table is маса (masa), and in Slovenian a table is miza and chair is stol.

The Russian for chair is стул (/stul/), which sounds even more like stool, and stool is табуретка (/taburʲetka/), which probably comes from the French word for stool, tabouret. The English word stool comes from the Old English stól (seat for one person), from the Proto-Germanic *stōlaz, probably from the Proto-Indo-European root *stō-/sta- (to stand). The Slavic words for table probably come from the same root.

Stool came to mean a small seat without arms or a back when the word chair was adopted from French, via the Middle English chaere/chaiere from the Old French chaëre from the Latin cathedra (seat), from the Greek καθέδρα (chair, especially the seat of a bishop, or a teacher’s or professor’s chair) from κατά (down) and ἑδ (sit). In modern French the word chaire means a pulpit or a university chair (professorship), while a normal chair that you sit on is a chaise.

The English word table comes from the the classical Latin word tabula (board, plank, writing/votive tablet, map, picture), and was influenced by the Anglo-Norman tabul/tabull (board, plank, writing table, picture). The origin of the Latin word tabula is uncertain.

Sources: OED, Reverso, Online Etymology Dictionary